1
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Adelhardt P, Koziol JA, Langheld A, Schmidt KP. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:401. [PMID: 38785650 PMCID: PMC11120707 DOI: 10.3390/e26050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 04/17/2024] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
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Affiliation(s)
| | | | | | - Kai P. Schmidt
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; (P.A.); (J.A.K.); (A.L.)
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2
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Numerical Interchain Mean-Field Theory for the Specific Heat of the Bimetallic Ferromagnetically Coupled Chain Compound MnNi(NO 2) 4(en) 2 (en = Ethylenediamine). Molecules 2022; 27:molecules27196546. [PMID: 36235083 PMCID: PMC9572235 DOI: 10.3390/molecules27196546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Revised: 09/25/2022] [Accepted: 09/28/2022] [Indexed: 11/16/2022] Open
Abstract
We present a detailed study of the field-dependent specific heat of the bimetallic ferromagnetically coupled chain compound MnNi(NO2)4(en)2, en = ethylenediamine. For this material, which in zero field orders antiferromagnetically below TN=2.45 K, small fields suppress magnetic order. Instead, in such fields, a double-peak-like structure in the temperature dependence of the specific heat is observed. We attribute this behavior to the existence of an acoustic and an optical mode in the spin-wave dispersion as a result of the existence of two different spins per unit cell. We compare our experimental data to numerical results for the specific heat obtained by exact diagonalization and Quantum Monte Carlo simulations for the alternating spin-chain model, using parameters that have been derived from the high-temperature behavior of the magnetic susceptibility. The interchain coupling is included in the numerical treatment at the mean-field level. We observe remarkable agreement between experiment and theory, including the ordering transition, using previously determined parameters. Furthermore, the observed strong effect of an applied magnetic field on the ordered state of MnNi(NO2)4(en)2 promises interesting magnetocaloric properties.
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3
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Rubín J, Arauzo A, Bartolomé E, Sedona F, Rancan M, Armelao L, Luzón J, Guidi T, Garlatti E, Wilhelm F, Rogalev A, Amann A, Spagna S, Bartolomé J, Bartolomé F. Origin of the Unusual Ground-State Spin S = 9 in a Cr 10 Single-Molecule Magnet. J Am Chem Soc 2022; 144:12520-12535. [PMID: 35759747 PMCID: PMC9979690 DOI: 10.1021/jacs.2c05453] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The molecular wheel [Cr10(OMe)20(O2CCMe3)10], abbreviated {Cr10}, with an unusual intermediate total spin S = 9 and non-negligible cluster anisotropy, D/kB = -0.045(2) K, is a rare case among wheels based on an even number of 3d-metals, which usually present an antiferromagnetic (AF) ground state (S = 0). Herein, we unveil the origin of such a behavior. Angular magnetometry measurements performed on a single crystal confirmed the axial anisotropic behavior of {Cr10}. For powder samples, the temperature dependence of the susceptibility plotted as χT(T) showed an overall ferromagnetic (FM) behavior down to 1.8 K, whereas the magnetization curve M(H) did not saturate at the expected 30 μB/fu for 10 FM coupled 3/2 spin Cr3+ ions, but to a much lower value, corresponding to S = 9. In addition, the X-ray magnetic circular dichroism (XMCD) measured at high magnetic field (170 kOe) and 7.5 K showed the polarization of the cluster moment up to 23 μB/fu. The magnetic results can be rationalized within a model, including the cluster anisotropy, in which the {Cr10} wheel is formed by two semiwheels, each with four Cr3+ spins FM coupled (JFM/kB = 2.0 K), separated by two Cr3+ ions AF coupled asymmetrically (J23/kB = J78/kB = -2.0 K; J34/kB = J89/kB = -0.25 K). Inelastic neutron scattering and heat capacity allowed us to confirm this model leading to the S = 9 ground state and first excited S = 8. Single-molecule magnet behavior with an activation energy of U/kB = 4.0(5) K in the absence of applied field was observed through ac susceptibility measurements down to 0.1 K. The intriguing magnetic behavior of {Cr10} arises from the detailed asymmetry in the molecule interactions produced by small-angle distortions in the angles of the Cr-O-Cr alkoxy bridges coupling the Cr3+ ions, as demonstrated by ab initio and density functional theory calculations, while the cluster anisotropy can be correlated to the single-ion anisotropies calculated for each Cr3+ ion in the wheel.
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Affiliation(s)
- Javier Rubín
- Instituto
de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain,Departamento
de Ciencia y Tecnología de Materiales y Fluidos, Universidad de Zaragoza, 50018 Zaragoza, Spain,
| | - Ana Arauzo
- Instituto
de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain,Servicio
de Medidas Físicas, Universidad de
Zaragoza, Pedro Cerbuna
12, 50009 Zaragoza, Spain,Departamento
de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Elena Bartolomé
- Escola
Universitària Salesiana de Sarrià (EUSS), Passeig Sant Joan Bosco 74, 08017 Barcelona, Spain,
| | - Francesco Sedona
- Dipartimento
di Scienze Chimiche, Università di
Padova, Via Marzolo 1, 35131 Padova, Italy
| | - Marzio Rancan
- Institute
of Condensed Matter Chemistry and Technologies for Energy (ICMATE),
National Research Council (CNR), c/o Department of Chemistry, University of Padova, via F. Marzolo 1, 35131 Padova, Italy
| | - Lidia Armelao
- Dipartimento
di Scienze Chimiche, Università di
Padova, Via Marzolo 1, 35131 Padova, Italy,Department
of Chemical Sciences and Materials Technologies (DSCTM), National Research Council (CNR), Piazzale A. Moro 7, 00185 Roma, Italy
| | - Javier Luzón
- Academia
General Militar, Centro Universitario de
la Defensa, 50090 Zaragoza, Spain
| | - Tatiana Guidi
- Physics
Division, School of Science and Technology, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino, MC, Italy,ISIS
Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, Oxfordshire, U.K.
| | - Elena Garlatti
- Dipartimento
di Science Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
| | - Fabrice Wilhelm
- ESRF − The European Synchrotron Radiation Facility, 71 Avenue des Martyrs CS40220, F-38043 Grenoble Cedex 09, France
| | - Andrei Rogalev
- ESRF − The European Synchrotron Radiation Facility, 71 Avenue des Martyrs CS40220, F-38043 Grenoble Cedex 09, France
| | - Andreas Amann
- Quantum Design Inc., San Diego, California 92121, United States
| | - Stefano Spagna
- Quantum Design Inc., San Diego, California 92121, United States
| | - Juan Bartolomé
- Instituto
de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain,Departamento
de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Fernando Bartolomé
- Instituto
de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain,Departamento
de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain,
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4
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Galeski S, Povarov KY, Blosser D, Gvasaliya S, Wawrzynczak R, Ollivier J, Gooth J, Zheludev A. LT Scaling in Depleted Quantum Spin Ladders. PHYSICAL REVIEW LETTERS 2022; 128:237201. [PMID: 35749184 DOI: 10.1103/physrevlett.128.237201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 05/02/2022] [Accepted: 05/10/2022] [Indexed: 06/15/2023]
Abstract
Using a combination of neutron scattering, calorimetry, quantum Monte Carlo simulations, and analytic results we uncover confinement effects in depleted, partially magnetized quantum spin ladders. We show that introducing nonmagnetic impurities into magnetized spin ladders leads to the emergence of a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger liquid (serving as the effective low-energy model). This results in universal LT scaling of staggered susceptibilities. Comparison of simulation results with experimental phase diagrams of prototypical spin ladder compounds bis(2,3-dimethylpyridinium)tetrabromocuprate(II) (DIMPY) and bis(piperidinium)tetrabromocuprate(II) (BPCB) yields excellent agreement.
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Affiliation(s)
- S Galeski
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40,01187 Dresden, Germany
| | - K Yu Povarov
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - D Blosser
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - S Gvasaliya
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - R Wawrzynczak
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40,01187 Dresden, Germany
- Institut Laue-Langevin, 6 rue Jules Horowitz, 38042 Grenoble, France
| | - J Ollivier
- Institut Laue-Langevin, 6 rue Jules Horowitz, 38042 Grenoble, France
| | - J Gooth
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40,01187 Dresden, Germany
| | - A Zheludev
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
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5
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Hong T, Ying T, Huang Q, Dissanayake SE, Qiu Y, Turnbull MM, Podlesnyak AA, Wu Y, Cao H, Liu Y, Umehara I, Gouchi J, Uwatoko Y, Matsuda M, Tennant DA, Chern GW, Schmidt KP, Wessel S. Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C 9H 18N 2CuBr 4. Nat Commun 2022; 13:3073. [PMID: 35654798 PMCID: PMC9163114 DOI: 10.1038/s41467-022-30769-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 05/14/2022] [Indexed: 11/12/2022] Open
Abstract
Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C9H18N2CuBr4. Single-crystal heat capacity and neutron diffraction measurements reveal that the Néel-ordered phase breaks down beyond a critical pressure of Pc ∼ 1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above Pc. There is a class of quantum phase transitions that do not fit into the traditional Landau paradigm, but are described in terms of fractionalized degrees of freedom and emergent gauge fields. Hong et al. find evidence of such a transition in a molecular spin-1/2 antiferromagnetic ladder compound under hydrostatic pressure.
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Affiliation(s)
- Tao Hong
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA.
| | - Tao Ying
- School of Physics, Harbin Institute of Technology, 150001, Harbin, China
| | - Qing Huang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, 37996, USA
| | - Sachith E Dissanayake
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14617, USA
| | - Yiming Qiu
- National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA
| | - Mark M Turnbull
- Carlson School of Chemistry and Biochemistry, Clark University, Worcester, MA, 01610, USA
| | - Andrey A Podlesnyak
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - Yan Wu
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - Huibo Cao
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - Yaohua Liu
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA.,Second Target Station, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - Izuru Umehara
- Department of Physics, Yokohama National University, Yokohama, 240-8501, Japan
| | - Jun Gouchi
- Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8581, Japan
| | - Yoshiya Uwatoko
- Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8581, Japan
| | - Masaaki Matsuda
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - David A Tennant
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, 37996, USA.,Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, 37996, USA
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA
| | - Kai P Schmidt
- Lehrstuhl für Theoretische Physik I, Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Staudtstrasse 7, Erlangen, D-91058, Germany
| | - Stefan Wessel
- Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
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6
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Lu TQ, Xu H, Cheng LT, Wang XT, Chen C, Cao L, Zhuang GL, Zheng J, Zheng XY. Family of Nanoclusters, Ln 33 (Ln = Sm/Eu) and Gd 32, Exhibiting Magnetocaloric Effects and Fluorescence Sensing for MnO 4. Inorg Chem 2022; 61:8861-8869. [PMID: 35653200 DOI: 10.1021/acs.inorgchem.2c00898] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
A family of nanoclusters, [Ln33(EDTA)12(OAc)2(CO3)4(μ3-OH)36(μ5-OH)4(H2O)38]·OAc·xH2O (x ≈ 50, Ln = Sm for 1; x ≈ 70, Ln = Eu for 2) and [Gd32(EDTA)12(OAc)2(C2O4)(CO3)2(μ3-OH)36(μ5-OH)4(H2O)36]·x(H2O) (x ≈ 70 for 3; H4EDTA = ethylene diamine tetraacetic acid), was prepared through the assembly of repeating subunits under the action of an anion template. The analysis of the structures showed that compounds 1 and 2 containing 33 Ln3+ ions were isostructural, which were constructed by three kinds of subunits in the presence of CO32- as an anion template, while compound 3 had a slightly different structure. Compound 3 containing 32 Gd3+ ions was formed by three types of subunits in the presence of CO32- and C2O42- as a mixed anion template. The CO32- anions came from the slow fixation of CO2 in the air. Meanwhile, one kind of high-nuclearity lanthanide clusters showed high chemical stability. The quantum Monte Carlo (QMC) calculation suggested that weak antiferromagnetic interactions were dominant between Gd3+ ions in 3. Magnetocaloric studies showed that compound 3 had a large entropy change of 43.0 J kg-1 K-1 at 2 K and 7 T. Surprisingly, compound 2 showed excellent recognition and detection effects for permanganate in aqueous solvents based on the fluorescence quenching phenomenon.
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Affiliation(s)
- Tian-Qi Lu
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
| | - Han Xu
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Department of Chemistry, iChEM, College of Chemistry and Chemical Engineering, Xiamen University, Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Lan-Tao Cheng
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
| | - Xue-Tao Wang
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
| | - Cheng Chen
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
| | - Lingyun Cao
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Department of Chemistry, iChEM, College of Chemistry and Chemical Engineering, Xiamen University, Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Gui-Lin Zhuang
- College of Chemical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
| | - Jun Zheng
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
| | - Xiu-Ying Zheng
- Institutes of Physical Science and Information Technology, Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education, Anhui University, Hefei 230601, China
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7
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Guo J, Sun J, Zhu X, Li CA, Guo H, Feng S. Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:035603. [PMID: 34663768 DOI: 10.1088/1361-648x/ac30b4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 10/18/2021] [Indexed: 06/13/2023]
Abstract
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
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Affiliation(s)
- Jiaojiao Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Junsong Sun
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Xingchuan Zhu
- Center for Basic Teaching and Experiment, Nanjing University of Science and Technology, Jiangyin 214443, People's Republic of China
| | - Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
| | - Huaiming Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing, 100875, People's Republic of China
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8
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Dupont M, Kvashnin YO, Shiranzaei M, Fransson J, Laflorencie N, Kantian A. Monolayer CrCl_{3} as an Ideal Test Bed for the Universality Classes of 2D Magnetism. PHYSICAL REVIEW LETTERS 2021; 127:037204. [PMID: 34328783 DOI: 10.1103/physrevlett.127.037204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
The monolayer halides CrX_{3} (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl_{3} has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl_{3} for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl_{3}, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl_{3} to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.
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Affiliation(s)
- M Dupont
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Y O Kvashnin
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
| | - M Shiranzaei
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
| | - J Fransson
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
| | - N Laflorencie
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - A Kantian
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
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9
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Zhu X, Guo J, Breuckmann NP, Guo H, Feng S. Quantum phase transitions of interacting bosons on hyperbolic lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:335602. [PMID: 34111850 DOI: 10.1088/1361-648x/ac0a1a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 06/10/2021] [Indexed: 06/12/2023]
Abstract
The effect of many-body interaction in curved space is studied based on the extended Bose-Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction asqin the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.
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Affiliation(s)
- Xingchuan Zhu
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
- Center for Basic Teaching and Experiment, Nanjing University of Science and Technology, Jiangyin 214443, People's Republic of China
| | - Jiaojiao Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Nikolas P Breuckmann
- Department of Physics and Astronomy, University College London, WC1E 6BT London, United Kingdom
| | - Huaiming Guo
- School of Physics, Beihang University, Beijing 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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10
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Zhou C, Yan Z, Wu HQ, Sun K, Starykh OA, Meng ZY. Amplitude Mode in Quantum Magnets via Dimensional Crossover. PHYSICAL REVIEW LETTERS 2021; 126:227201. [PMID: 34152175 DOI: 10.1103/physrevlett.126.227201] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 12/15/2020] [Accepted: 05/03/2021] [Indexed: 05/10/2023]
Abstract
We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model. The amplitude mode is observed to emerge in the longitudinal spin susceptibility in the presence of a weak symmetry-breaking staggered field. A conventional measure of the amplitude mode in higher dimensions, the singlet bond mode, is found to appear at a lower than the amplitude mode frequency. We identify these two excitations with the second (first) breather of the sine-Gordon theory, correspondingly. In contrast to higher-dimensional systems, the amplitude and bond order fluctuations are found to carry significant spectral weight in the quasi-1D limit.
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Affiliation(s)
- Chengkang Zhou
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Zheng Yan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China
| | - Han-Qing Wu
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Oleg A Starykh
- Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
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11
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Zhou XG, Yao Y, Matsuda YH, Ikeda A, Matsuo A, Kindo K, Tanaka H. Particle-Hole Symmetry Breaking in a Spin-Dimer System TlCuCl_{3} Observed at 100 T. PHYSICAL REVIEW LETTERS 2020; 125:267207. [PMID: 33449724 DOI: 10.1103/physrevlett.125.267207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
The entire magnetization process of TlCuCl_{3} has been experimentally investigated up to 100 T employing the single-turn technique. The upper critical field H_{c2} is observed to be 86.1 T at 2 K. A convex slope of the M-H curve between the lower and upper critical fields (H_{c1} and H_{c2}) is clearly observed, which indicates that a particle-hole symmetry is broken in TlCuCl_{3}. By quantum Monte Carlo simulation and the bond-operator theory method, we find that the particle-hole symmetry breaking results from strong interdimer interactions.
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Affiliation(s)
- X-G Zhou
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Yuan Yao
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Y H Matsuda
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - A Ikeda
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - A Matsuo
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - K Kindo
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - H Tanaka
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
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12
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Ying T, Schmidt KP, Wessel S. Higgs Mode of Planar Coupled Spin Ladders and its Observation in C_{9}H_{18}N_{2}CuBr_{4}. PHYSICAL REVIEW LETTERS 2019; 122:127201. [PMID: 30978068 DOI: 10.1103/physrevlett.122.127201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Indexed: 06/09/2023]
Abstract
Polarized inelastic neutron scattering experiments recently identified the amplitude (Higgs) mode in C_{9}H_{18}N_{2}CuBr_{4}, a two-dimensional near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin structure factor of such planar coupled spin-ladder systems using large-scale quantum Monte Carlo simulations. This allows us to provide a quantitative account of the experimental neutron scattering data within a consistent quantum spin model. Moreover, we trace the details of the continuous evolution of the amplitude mode from a two-particle bound state of coupled ladders in the classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with fully restored SU(2) symmetry, where it gets overdamped by the two-magnon continuum in neutron scattering.
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Affiliation(s)
- T Ying
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
- Department of Physics, Harbin Institute of Technology, 150001 Harbin, China
| | - K P Schmidt
- Institut für Theoretische Physik, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - S Wessel
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
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13
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Stapmanns J, Corboz P, Mila F, Honecker A, Normand B, Wessel S. Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet. PHYSICAL REVIEW LETTERS 2018; 121:127201. [PMID: 30296119 DOI: 10.1103/physrevlett.121.127201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Indexed: 06/08/2023]
Abstract
We consider the finite-temperature phase diagram of the S=1/2 frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity.
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Affiliation(s)
- J Stapmanns
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
| | - P Corboz
- Institute for Theoretical Physics and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - F Mila
- Institute of Physics, Ecole Polytechnique Fédérale Lausanne (EPFL), 1015 Lausanne, Switzerland
| | - A Honecker
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, France
| | - B Normand
- Neutrons and Muons Research Division, Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland
| | - S Wessel
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
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14
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Wehinger B, Fiolka C, Lanza A, Scatena R, Kubus M, Grockowiak A, Coniglio WA, Graf D, Skoulatos M, Chen JH, Gukelberger J, Casati N, Zaharko O, Macchi P, Krämer KW, Tozer S, Mudry C, Normand B, Rüegg C. Giant Pressure Dependence and Dimensionality Switching in a Metal-Organic Quantum Antiferromagnet. PHYSICAL REVIEW LETTERS 2018; 121:117201. [PMID: 30265101 DOI: 10.1103/physrevlett.121.117201] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Indexed: 06/08/2023]
Abstract
We report an extraordinary pressure dependence of the magnetic interactions in the metal-organic system [CuF_{2}(H_{2}O)_{2}]_{2}pyrazine. At zero pressure, this material realizes a quasi-two-dimensional spin-1/2 square-lattice Heisenberg antiferromagnet. By high-pressure, high-field susceptibility measurements we show that the dominant exchange parameter is reduced continuously by a factor of 2 on compression. Above 18 kbar, a phase transition occurs, inducing an orbital re-ordering that switches the dimensionality, transforming the quasi-two-dimensional lattice into weakly coupled chains. We explain the microscopic mechanisms for both phenomena by combining detailed x-ray and neutron diffraction studies with quantitative modeling using spin-polarized density functional theory.
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Affiliation(s)
- B Wehinger
- Department of Quantum Matter Physics, University of Geneva, 24, Quai Ernest Ansermet, CH-1211 Genève, Switzerland
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - C Fiolka
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - A Lanza
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - R Scatena
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - M Kubus
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - A Grockowiak
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - W A Coniglio
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - D Graf
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - M Skoulatos
- Heinz-Maier-Leibnitz Zentrum and Physics Department, Technische Universität München, Lichtenbergstrasse 1, 85748 Garching, Germany
| | - J-H Chen
- Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
- Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - J Gukelberger
- Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
- Département de Physique and Institut Quantique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
| | - N Casati
- Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - O Zaharko
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - P Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - K W Krämer
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - S Tozer
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | - C Mudry
- Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - B Normand
- Neutrons and Muons Research Division, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
| | - Ch Rüegg
- Department of Quantum Matter Physics, University of Geneva, 24, Quai Ernest Ansermet, CH-1211 Genève, Switzerland
- Neutrons and Muons Research Division, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
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15
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Becker J, Wessel S. Diagnosing Fractionalization from the Spin Dynamics of Z_{2} Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2018; 121:077202. [PMID: 30169092 DOI: 10.1103/physrevlett.121.077202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Indexed: 06/08/2023]
Abstract
Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice spin-1/2 model, which is known to harbor an extended Z_{2} quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the Z_{2} quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.
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Affiliation(s)
- Jonas Becker
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
| | - Stefan Wessel
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
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16
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Rubio-García A, Alcoba DR, Capuzzi P, Dukelsky J. Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models. J Chem Theory Comput 2018; 14:4183-4192. [PMID: 29906104 DOI: 10.1021/acs.jctc.8b00387] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.
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Affiliation(s)
- A Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain
| | - D R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires , Argentina.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , Ciudad Universitaria , 1428 Buenos Aires , Argentina
| | - P Capuzzi
- Departamento de Física, Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires , Argentina.,Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas , Ciudad Universitaria , 1428 Buenos Aires , Argentina
| | - J Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123 , 28006 Madrid , Spain
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17
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Weber M, Assaad FF, Hohenadler M. Directed-Loop Quantum Monte Carlo Method for Retarded Interactions. PHYSICAL REVIEW LETTERS 2017; 119:097401. [PMID: 28949554 DOI: 10.1103/physrevlett.119.097401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Indexed: 06/07/2023]
Abstract
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to 1282 sites.
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Affiliation(s)
- Manuel Weber
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
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18
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Danilovich IL, Karpova EV, Morozov IV, Ushakov AV, Streltsov SV, Shakin AA, Volkova OS, Zvereva EA, Vasiliev AN. Spin-singlet Quantum Ground State in Zigzag Spin Ladder Cu(CF 3 COO) 2. Chemphyschem 2017; 18:2482-2486. [PMID: 28726353 DOI: 10.1002/cphc.201700707] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2017] [Revised: 07/18/2017] [Indexed: 11/09/2022]
Abstract
The copper salt of trifluoroacetic acid, Cu(CF3 COO)2 , offers a new platform to investigate the quantum ground states of low-dimensional magnets. In practice, it realizes the ideal case of a solid hosting essentially isolated magnetic monolayers. These entities are constituted by well-separated two-leg half-integer spin ladders organized in a zigzag fashion. The ladders are comprised of dimeric units of edge-sharing tetragonal pyramids coupled through carbon ions. The spin-gap state in this compound was revealed by static and dynamic magnetic measurements. No indications of long range magnetic ordering down to liquid helium temperature were obtained in specific heat measurements. First principles calculations allow estimation of the main exchange interaction parameters, J⊥ =176 K and J∥ =12 K, consistent with the weakly interacting dimers model.
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Affiliation(s)
| | | | | | - Alexey V Ushakov
- Institute of Metal Physics, Russian Academy of Sciences, Ekaterinburg, 620041, Russia
| | - Sergey V Streltsov
- Institute of Metal Physics, Russian Academy of Sciences, Ekaterinburg, 620041, Russia.,Ural Federal University, Ekaterinburg, 620002, Russia
| | - Alexander A Shakin
- National University of Science and Technology "MISiS", Moscow, 119049, Russia
| | - Olga S Volkova
- Moscow State University, Moscow, 119991, Russia.,Ural Federal University, Ekaterinburg, 620002, Russia.,National University of Science and Technology "MISiS", Moscow, 119049, Russia
| | - Elena A Zvereva
- Moscow State University, Moscow, 119991, Russia.,National Research South Ural State University, Chelyabinsk, 454080, Russia
| | - Alexander N Vasiliev
- Moscow State University, Moscow, 119991, Russia.,National University of Science and Technology "MISiS", Moscow, 119049, Russia.,National Research South Ural State University, Chelyabinsk, 454080, Russia
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19
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Lohöfer M, Wessel S. Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets. PHYSICAL REVIEW LETTERS 2017; 118:147206. [PMID: 28430505 DOI: 10.1103/physrevlett.118.147206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Indexed: 06/07/2023]
Abstract
By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of sqrt[2] to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. Its width is observed to vanish proportional to the Higgs mass in the accessible proximity to the quantum critical point.
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Affiliation(s)
- M Lohöfer
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
| | - S Wessel
- Institut für Theoretische Festkörperphysik, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
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20
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Broecker P, Trebst S. Numerical stabilization of entanglement computation in auxiliary-field quantum Monte Carlo simulations of interacting many-fermion systems. Phys Rev E 2016; 94:063306. [PMID: 28085385 DOI: 10.1103/physreve.94.063306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2016] [Indexed: 06/06/2023]
Abstract
In the absence of a fermion sign problem, auxiliary-field (or determinantal) quantum Monte Carlo (DQMC) approaches have long been the numerical method of choice for unbiased, large-scale simulations of interacting many-fermion systems. More recently, the conceptual scope of this approach has been expanded by introducing ingenious schemes to compute entanglement entropies within its framework. On a practical level, these approaches, however, suffer from a variety of numerical instabilities that have largely impeded their applicability. Here we report on a number of algorithmic advances to overcome many of these numerical instabilities and significantly improve the calculation of entanglement measures in the zero-temperature projective DQMC approach, ultimately allowing us to reach similar system sizes as for the computation of conventional observables. We demonstrate the applicability of this improved DQMC approach by providing an entanglement perspective on the quantum phase transition from a magnetically ordered Mott insulator to a band insulator in the bilayer square lattice Hubbard model at half filling.
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Affiliation(s)
- Peter Broecker
- Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany
| | - Simon Trebst
- Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany
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21
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Alet F, Damle K, Pujari S. Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets. PHYSICAL REVIEW LETTERS 2016; 117:197203. [PMID: 27858437 DOI: 10.1103/physrevlett.117.197203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2016] [Indexed: 06/06/2023]
Abstract
We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.
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Affiliation(s)
- Fabien Alet
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France
| | - Kedar Damle
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India
| | - Sumiran Pujari
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA
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22
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Huffman E, Chandrasekharan S. Solution to sign problems in models of interacting fermions and quantum spins. Phys Rev E 2016; 94:043311. [PMID: 27841597 DOI: 10.1103/physreve.94.043311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2016] [Indexed: 06/06/2023]
Abstract
We show that solutions to fermion sign problems that are found in the formulation where the path integral is expanded in powers of the interaction in continuous time can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the world-line representation of quantum spins. Combining this idea with meron-cluster methods, we are able to further extend the class of models that are solvable. We demonstrate these solutions to sign problems by considering several examples of strongly correlated systems that contain the physics of semimetals, insulators, superfluidity, and antiferromagnetism.
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Affiliation(s)
- Emilie Huffman
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA
| | - Shailesh Chandrasekharan
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA
- Center for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India
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23
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Pchelkina ZV, Solovyev IV. First-principles investigation of exchange interactions in quasi-one-dimensional antiferromagnet CaV2O4. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:026001. [PMID: 25501902 DOI: 10.1088/0953-8984/27/2/026001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The effects of orbital degrees of freedom on the exchange interactions in a quasi-one-dimensional spin-1 antiferromagnet CaV2O4 are systematically studied. For this purpose a realistic low-energy electron model with the parameters derived from the first-principles calculations is constructed in the Wannier basis for the t2g bands. The exchange interactions are calculated using both the theory of infinitesimal spin rotations near the mean-field ground state and the superexchange model, which provide a consistent description. The obtained behaviour of exchange interactions differs substantially from the previously proposed phenomenological picture based on magnetic measurements and structural considerations, namely: (i) despite the quasi-one-dimensional character of the crystal structure, consisting of the zigzag chains of the edge-sharing VO6 octahedra, the electronic structure is essentially three-dimensional, that leads to finite interactions between the chains; (ii) the exchange interactions along the legs of the chains appear to dominate; and (iii) there is a substantial difference in exchange interactions in two crystallographically inequivalent chains. The combination of these three factors successfully reproduces the behaviour of experimental magnetic susceptibility.
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Affiliation(s)
- Z V Pchelkina
- M N Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, 620137, Ekaterinburg, Russia. Theoretical Physics and Applied Mathematics Department, Institute of Physics and Technology, Ural Federal University, Ekaterinburg 620002, Russia
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24
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Evidence of a field-induced Berezinskii-Kosterlitz-Thouless scenario in a two-dimensional spin-dimer system. Nat Commun 2014; 5:5169. [PMID: 25346338 DOI: 10.1038/ncomms6169] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 09/08/2014] [Indexed: 11/08/2022] Open
Abstract
Two-dimensional (2D) systems with continuous symmetry lack conventional long-range order because of thermal fluctuations. Instead, as pointed out by Berezinskii, Kosterlitz and Thouless (BKT), 2D systems may exhibit so-called topological order driven by the binding of vortex-antivortex pairs. Signatures of the BKT mechanism have been observed in thin films, specially designed heterostructures, layered magnets and trapped atomic gases. Here we report on an alternative approach for studying BKT physics by using a chemically constructed multilayer magnet. The novelty of this approach is to use molecular-based pairs of spin S=½ ions, which, by the application of a magnetic field, provide a gas of magnetic excitations. On the basis of measurements of the magnetic susceptibility and specific heat on a so-designed material, combined with density functional theory and quantum Monte Carlo calculations, we conclude that these excitations have a distinct 2D character, consistent with a BKT scenario, implying the emergence of vortices and antivortices.
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25
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Körmann F, Grabowski B, Dutta B, Hickel T, Mauger L, Fultz B, Neugebauer J. Temperature dependent magnon-phonon coupling in bcc Fe from theory and experiment. PHYSICAL REVIEW LETTERS 2014; 113:165503. [PMID: 25361267 DOI: 10.1103/physrevlett.113.165503] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2014] [Indexed: 06/04/2023]
Abstract
An ab initio based framework for quantitatively assessing the phonon contribution due to magnon-phonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnon-phonon interaction is an order of magnitude larger than the phonon shift due to lattice expansion, demonstrating the strong impact of magnetic short-range order even significantly above the Curie temperature. The framework closes the previous simulation gap between the ferro- and paramagnetic limits.
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Affiliation(s)
- F Körmann
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
| | - B Grabowski
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
| | - B Dutta
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
| | - T Hickel
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
| | - L Mauger
- California Institute of Technology, W. M. Keck Laboratory 138-78, Pasadena, California 91125, USA
| | - B Fultz
- California Institute of Technology, W. M. Keck Laboratory 138-78, Pasadena, California 91125, USA
| | - J Neugebauer
- Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany
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Palumbo M, Fries SG, Dal Corso A, Kürmann F, Hickel T, Neugebauer J. Reliability evaluation of thermophysical properties from first-principles calculations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:335401. [PMID: 25071092 DOI: 10.1088/0953-8984/26/33/335401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Thermophysical properties, such as heat capacity, bulk modulus and thermal expansion, are of great importance for many technological applications and are traditionally determined experimentally. With the rapid development of computational methods, however, first-principles computed temperature-dependent data are nowadays accessible. We evaluate various computational realizations of such data in comparison to the experimental scatter. The work is focussed on the impact of different first-principles codes (QUANTUM ESPRESSO and VASP), pseudopotentials (ultrasoft and projector augmented wave) as well as phonon determination methods (linear response and direct force constant method) on these properties. Based on the analysis of data for two pure elements, Cr and Ni, consequences for the reliability of temperature-dependent first-principles data in computational thermodynamics are discussed.
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Affiliation(s)
- Mauro Palumbo
- ICAMS, Ruhr University Bochum, Universitátsstr. 150, D-44801 Bochum, Germany
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Bonnes L, Hazzard KRA, Manmana SR, Rey AM, Wessel S. Adiabatic loading of one-dimensional SU(N) alkaline-earth-atom fermions in optical lattices. PHYSICAL REVIEW LETTERS 2012; 109:205305. [PMID: 23215502 DOI: 10.1103/physrevlett.109.205305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Indexed: 06/01/2023]
Abstract
Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.
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Affiliation(s)
- Lars Bonnes
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria.
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Barthel T, Hübener R. Solving condensed-matter ground-state problems by semidefinite relaxations. PHYSICAL REVIEW LETTERS 2012; 108:200404. [PMID: 23003130 DOI: 10.1103/physrevlett.108.200404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 01/07/2012] [Indexed: 06/01/2023]
Abstract
We present a generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite programs (SDP). These can be solved efficiently, yielding strict lower bounds to the ground-state energy and approximations to the few-particle Green's functions. As the method is applicable for all particle statistics, it represents, in particular, a novel route for the study of strongly correlated fermionic and frustrated spin systems in D>1 spatial dimensions. It is demonstrated for the XXZ model and the Hubbard model of spinless fermions. The results are compared against exact solutions, quantum Monte Carlo calculations, and Anderson bounds, showing the competitiveness of the SDP method.
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Affiliation(s)
- Thomas Barthel
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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32
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Bonnes L, Wessel S. Pair superfluidity of three-body constrained bosons in two dimensions. PHYSICAL REVIEW LETTERS 2011; 106:185302. [PMID: 21635100 DOI: 10.1103/physrevlett.106.185302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2011] [Revised: 03/22/2011] [Indexed: 05/30/2023]
Abstract
We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first order to a continuous transition of the dilute Bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.
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Affiliation(s)
- Lars Bonnes
- Institut für Theoretische Physik III, Universität Stuttgart, Germany
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Shiroka T, Casola F, Glazkov V, Zheludev A, Prša K, Ott HR, Mesot J. Distribution of NMR relaxations in a random Heisenberg chain. PHYSICAL REVIEW LETTERS 2011; 106:137202. [PMID: 21517418 DOI: 10.1103/physrevlett.106.137202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2010] [Revised: 03/07/2011] [Indexed: 05/30/2023]
Abstract
NMR measurements of the (29)Si spin-lattice relaxation time T(1) were used to probe the spin-1/2 random Heisenberg chain compound BaCu(2)(Si(1-x)Ge(x))(2)O(7). Remarkable differences between the pure (x=0) and the fully random (x=0.5) cases are observed, indicating that randomness generates a distribution of local magnetic relaxations. This distribution, which is reflected in a stretched exponential NMR relaxation, exhibits a progressive broadening with decreasing temperature, caused by a growing inequivalence of magnetic sites. Compelling independent evidence for the influence of randomness is also obtained from magnetization data and Monte Carlo calculations. These results suggest the formation of random-singlet states in this class of materials, as previously predicted by theory.
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Affiliation(s)
- T Shiroka
- Laboratorium für Festkörperphysik, ETH Hönggerberg, CH-8093 Zürich, Switzerland
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34
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Cramer M, Plenio MB, Wunderlich H. Measuring entanglement in condensed matter systems. PHYSICAL REVIEW LETTERS 2011; 106:020401. [PMID: 21405204 DOI: 10.1103/physrevlett.106.020401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2010] [Revised: 11/17/2010] [Indexed: 05/30/2023]
Abstract
We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.
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Affiliation(s)
- M Cramer
- Institut für Theoretische Physik, Albert-Einstein Allee 11, Universität Ulm, Ulm, Germany
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35
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Suwa H, Todo S. Markov chain Monte Carlo method without detailed balance. PHYSICAL REVIEW LETTERS 2010; 105:120603. [PMID: 20867621 DOI: 10.1103/physrevlett.105.120603] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2010] [Indexed: 05/29/2023]
Abstract
We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.
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Affiliation(s)
- Hidemaro Suwa
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
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36
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Schwandt D, Alet F, Capponi S. Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions. PHYSICAL REVIEW LETTERS 2009; 103:170501. [PMID: 19905737 DOI: 10.1103/physrevlett.103.170501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2009] [Revised: 09/14/2009] [Indexed: 05/28/2023]
Abstract
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
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Affiliation(s)
- David Schwandt
- Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), F-31062 Toulouse, France
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37
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Schmidt KP, Dorier J, Läuchli AM. Solids and supersolids of three-body interacting polar molecules on an optical lattice. PHYSICAL REVIEW LETTERS 2008; 101:150405. [PMID: 18999578 DOI: 10.1103/physrevlett.101.150405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2008] [Indexed: 05/27/2023]
Abstract
We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Büchler et al. [Nature Phys. 3, 726 (2007)]. To this end, quantum Monte Carlo simulations, exact diagonalization, and a semiclassical approach are used to explore hard-core bosons on the 2D square lattice which interact solely by long-ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.
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Affiliation(s)
- Kai P Schmidt
- Lehrstuhl für theoretische Physik I, Otto-Hahn-Str. 4, TU Dortmund, D-44221 Dortmund, Germany.
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38
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Wenzel S, Bogacz L, Janke W. Evidence for an unconventional universality class from a two-dimensional dimerized quantum heisenberg model. PHYSICAL REVIEW LETTERS 2008; 101:127202. [PMID: 18851407 DOI: 10.1103/physrevlett.101.127202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2008] [Revised: 07/10/2008] [Indexed: 05/26/2023]
Abstract
The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.
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Affiliation(s)
- Sandro Wenzel
- Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Leipzig, Germany.
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39
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Schmidt KP, Dorier J, Läuchli AM, Mila F. Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets. PHYSICAL REVIEW LETTERS 2008; 100:090401. [PMID: 18352679 DOI: 10.1103/physrevlett.100.090401] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2007] [Revised: 10/25/2007] [Indexed: 05/26/2023]
Abstract
We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization, respectively. Using quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove, in particular, that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.
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Affiliation(s)
- K P Schmidt
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland.
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40
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Kao YJ, Melko RG. Short-loop algorithm for quantum Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036708. [PMID: 18517558 DOI: 10.1103/physreve.77.036708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2007] [Revised: 12/12/2007] [Indexed: 05/26/2023]
Abstract
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where nonlocal cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase simulation efficiency in cases where conventional loops become very large, do not close altogether, or otherwise behave poorly. We demonstrate and characterize some aspects of the short loop on a square lattice spin-1/2 XXZ model where, remarkably, a significant increase in simulation efficiency is observed in some parameter regimes. The simplicity of the model provides a prototype for the use of short loops on more complicated quantum systems.
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Affiliation(s)
- Ying-Jer Kao
- Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan.
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41
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White SR, Chernyshev AL. Neél order in square and triangular lattice Heisenberg models. PHYSICAL REVIEW LETTERS 2007; 99:127004. [PMID: 17930545 DOI: 10.1103/physrevlett.99.127004] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2007] [Indexed: 05/25/2023]
Abstract
We show that the density matrix renormalization group can be used to study magnetic ordering in two-dimensional spin models. Local quantities should be extrapolated with the truncation error, not with its square root. We introduce sequences of clusters, using cylindrical boundary conditions with pinning fields, which provide for rapidly converging finite-size scaling. We determine the magnetization for both the square and triangular Heisenberg lattices with errors comparable to the best alternative approaches.
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Affiliation(s)
- Steven R White
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
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42
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Maeda Y, Hotta C, Oshikawa M. Universal temperature dependence of the magnetization of gapped spin chains. PHYSICAL REVIEW LETTERS 2007; 99:057205. [PMID: 17930786 DOI: 10.1103/physrevlett.99.057205] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2007] [Revised: 05/30/2007] [Indexed: 05/25/2023]
Abstract
A Haldane chain under applied field is analyzed numerically, and a clear minimum of magnetization is observed as a function of temperature. We elucidate its origin using the effective theory near the critical field and propose a simple method to estimate the gap from the magnetization at finite temperatures. We also demonstrate that there exists a relation between the temperature dependence of the magnetization and the field dependence of the spin-wave velocity. Our arguments are universal for general axially symmetric one-dimensional spin systems.
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Affiliation(s)
- Yoshitaka Maeda
- Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia, V6T 1Z1 Canada
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43
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Schneider RT, Landee CP, Turnbull MM, Awwadi FF, Twamley B. Copper azine compounds: Synthesis, structure and magnetic analyses of Cu(phenazine)Cl2, (phenazinium)2CuCl4·H2O, and [Cu(phenazine)Cl2·H2O]2. Polyhedron 2007. [DOI: 10.1016/j.poly.2006.09.019] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Kollath C, Läuchli AM, Altman E. Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model. PHYSICAL REVIEW LETTERS 2007; 98:180601. [PMID: 17501552 DOI: 10.1103/physrevlett.98.180601] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2006] [Indexed: 05/15/2023]
Abstract
We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.
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Affiliation(s)
- Corinna Kollath
- Université de Genève, 24 Quai Ernest-Ansermet, CH-1211 Genève, Switzerland
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45
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Nohadani O, Wessel S, Haas S. Bose-glass phases in disordered quantum magnets. PHYSICAL REVIEW LETTERS 2005; 95:227201. [PMID: 16384258 DOI: 10.1103/physrevlett.95.227201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2005] [Indexed: 05/05/2023]
Abstract
In disordered spin systems with antiferromagnetic Heisenberg exchange, transitions into and out of a magnetic-field-induced ordered phase pass through unique regimes. Using quantum Monte Carlo simulations to study the zero-temperature behavior, these intermediate regions are determined to be Bose-glass phases. The localization of field-induced triplons causes a finite compressibility and, hence, glassiness in the disordered phase.
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Affiliation(s)
- Omid Nohadani
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484, USA
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46
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Gimperlein H, Wessel S, Schmiedmayer J, Santos L. Ultracold atoms in optical lattices with random on-site interactions. PHYSICAL REVIEW LETTERS 2005; 95:170401. [PMID: 16383798 DOI: 10.1103/physrevlett.95.170401] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2005] [Indexed: 05/05/2023]
Abstract
We consider the physics of lattice bosons affected by disordered on-site interparticle interactions. Characteristic qualitative changes in the zero-temperature phase diagram are observed when compared to the case of randomness in the chemical potential. The Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards formation of a Bose glass leading to a possibly nontrivial tricritical point. We discuss feasible experimental realizations of our scenario in the context of ultracold atoms on optical lattices.
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Affiliation(s)
- H Gimperlein
- Institut für Theoretische Physik III, Universität Stuttgart, Pfaffenwaldring 57 V, D-70550 Stuttgart, Germany
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47
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Wessel S, Troyer M. Supersolid hard-core bosons on the triangular lattice. PHYSICAL REVIEW LETTERS 2005; 95:127205. [PMID: 16197105 DOI: 10.1103/physrevlett.95.127205] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2005] [Indexed: 05/04/2023]
Abstract
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
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Affiliation(s)
- Stefan Wessel
- Institut für Theoretische Physik III, Universität Stuttgart, 70550 Stuttgart, Germany
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48
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Melko RG, Sandvik AW. Stochastic series expansion algorithm for the S = 1/2 XY model with four-site ring exchange. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:026702. [PMID: 16196746 DOI: 10.1103/physreve.72.026702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2004] [Revised: 05/13/2005] [Indexed: 05/04/2023]
Abstract
We describe a stochastic series expansion quantum Monte Carlo method for a two-dimensional S = 1/2 XY model (or, equivalently, hard-core bosons at half filling) which in addition to the standard pair interaction J includes a four-site term K that flips spins on a square plaquette. The model has three ordered ground state phases; for K/J approximately < or = 8 it has long-range xy spin order (superfluid bosons), for K/J approximately > or = 15 it has staggered spin order in the z direction (charge-density wave), and between these phases it is in a state with columnar order in the bond and plaquette energy densities. We discuss an implementation of directed-loop updates for the SSE simulations of this model and also introduce a "multibranch" cluster update which significantly reduces the autocorrelation times for large K/J. In addition to the pure J-K model, which in the z basis has only off-diagonal terms, we also discuss modifications of the algorithm needed when various diagonal interactions are included.
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Affiliation(s)
- Roger G Melko
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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