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Liu ZH, Da Liao Y, Pan G, Song M, Zhao J, Jiang W, Jian CM, You YZ, Assaad FF, Meng ZY, Xu C. Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation. PHYSICAL REVIEW LETTERS 2024; 132:156503. [PMID: 38683001 DOI: 10.1103/physrevlett.132.156503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 11/22/2023] [Accepted: 03/23/2024] [Indexed: 05/01/2024]
Abstract
The "symmetric mass generation" (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true (2+1)d unitary conformal field theory.
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Affiliation(s)
- Zi Hong Liu
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Yuan Da Liao
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Gaopei Pan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Menghan Song
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Jiarui Zhao
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Weilun Jiang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
| | - Chao-Ming Jian
- Department of Physics, Cornell University, Ithaca, New York, USA
| | - Yi-Zhuang You
- Department of Physics, University of California, San Diego, California 92093, USA
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - 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
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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2
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Bonati C, Pelissetto A, Vicari E. Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields. Phys Rev E 2024; 109:044146. [PMID: 38755906 DOI: 10.1103/physreve.109.044146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2024] [Accepted: 04/01/2024] [Indexed: 05/18/2024]
Abstract
We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge Q≥2 is minimally coupled with a compact U(1) gauge field. Their phase diagram presents two phases separated by a transition line where static charges q, with q
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Affiliation(s)
- Claudio Bonati
- Dipartimento di Fisica dell'Università di Pisa and INFN Sezione di Pisa, I-56127 Pisa, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma Sapienza and INFN Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa, I-56127 Pisa, Italy
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3
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Bonati C, Pelissetto A, Vicari E. Coulomb-Higgs phase transition of three-dimensional lattice Abelian Higgs gauge models with noncompact gauge variables and gauge fixing. Phys Rev E 2023; 108:044125. [PMID: 37978683 DOI: 10.1103/physreve.108.044125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Accepted: 08/08/2023] [Indexed: 11/19/2023]
Abstract
We study the critical behavior of three-dimensional (3D) lattice Abelian Higgs (AH) gauge models with noncompact gauge variables and multicomponent complex scalar fields, along the transition line between the Coulomb and Higgs phases. Previous works that focused on gauge-invariant correlations provided evidence that, for a sufficiently large number of scalar components, these transitions are continuous and associated with the stable charged fixed point of the renormalization-group flow of the 3D AH field theory (scalar electrodynamics), in which charged scalar matter is minimally coupled with an electromagnetic field. Here we extend these studies by considering gauge-dependent correlations of the gauge and matter fields, in the presence of two different gauge fixings, the Lorenz and the axial gauge fixing. Our results for N=25 are definitely consistent with the predictions of the AH field theory and therefore provide additional evidence for the characterization of the 3D AH transitions along the Coulomb-Higgs line as charged transitions in the AH field-theory universality class. Moreover, our results give additional insights on the role of the gauge fixing at charged transitions. In particular, we show that scalar correlations are critical only if a hard Lorenz gauge fixing is imposed.
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Affiliation(s)
- Claudio Bonati
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma Sapienza and INFN Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
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4
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Shu YR, Jian SK, Yin S. Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time. PHYSICAL REVIEW LETTERS 2022; 128:020601. [PMID: 35089734 DOI: 10.1103/physrevlett.128.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 10/07/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We explicitly show the deconfinement dynamic process and identify that it is the spinon confinement length, rather than the usual correlation length, that increases proportionally to the time. Moreover, we find that, in the relaxation process, the order parameters of the Néel and the valence-bond-solid orders can be controlled by different length scales, although they satisfy the same equilibrium scaling forms. A dual dynamic scaling theory is then proposed. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems. Possible realizations in foreseeable quantum computers are also discussed.
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Affiliation(s)
- Yu-Rong Shu
- School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China
| | - Shao-Kai Jian
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shuai Yin
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
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5
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Cai X, Li ZX, Yao H. Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study. PHYSICAL REVIEW LETTERS 2021; 127:247203. [PMID: 34951814 DOI: 10.1103/physrevlett.127.247203] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 05/22/2021] [Accepted: 10/28/2021] [Indexed: 06/14/2023]
Abstract
Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.
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Affiliation(s)
- Xun Cai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zi-Xiang Li
- Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
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Yang S, Xu JB. Quantum entanglement and criticality in a one-dimensional deconfined quantum critical point. Phys Rev E 2021; 104:064121. [PMID: 35030944 DOI: 10.1103/physreve.104.064121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 12/03/2021] [Indexed: 06/14/2023]
Abstract
We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.
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Affiliation(s)
- Sheng Yang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jing-Bo Xu
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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7
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Bonati C, Pelissetto A, Vicari E. Higher-charge three-dimensional compact lattice Abelian-Higgs models. Phys Rev E 2021; 102:062151. [PMID: 33466077 DOI: 10.1103/physreve.102.062151] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 12/14/2020] [Indexed: 11/07/2022]
Abstract
We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N≥2 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., N=2 and N=25.
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Affiliation(s)
- Claudio Bonati
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma Sapienza and INFN, Sezione di Roma I, P.le A. Moro 2, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
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8
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Pelissetto A, Vicari E. Three-dimensional monopole-free CP^{N-1} models. Phys Rev E 2020; 101:062136. [PMID: 32688618 DOI: 10.1103/physreve.101.062136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Accepted: 06/04/2020] [Indexed: 06/11/2023]
Abstract
We investigate the phase diagram and the nature of the phase transitions of three-dimensional monopole-free CP^{N-1} models, characterized by a global U(N) symmetry, a U(1) gauge symmetry, and the absence of monopoles. We present numerical analyses based on Monte Carlo simulations for N=2, 4, 10, 15, and 25. We observe a finite-temperature transition in all cases, related to the condensation of a local gauge-invariant order parameter. For N=2 we are unable to draw any definite conclusion on the nature of the transition. The results may be interpreted in terms of either a weak first-order transition or a continuous transition with anomalously large scaling corrections. However, the results allow us to exclude that the transition belongs to the O(3) vector universality class, as it occurs in the standard three-dimensional CP^{1} model without monopole suppression. For N=4,10,and15, the transition is of first order, and significantly weaker than that observed in the presence of monopoles. For N=25 the results are consistent with a conventional continuous transition. We compare our results with the existing literature and with the predictions of different field-theory approaches. They are consistent with the scenario in which the model undergoes continuous transitions for large values of N, including N=∞, in agreement with analytic large-N calculations for the N-component Abelian-Higgs model.
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Affiliation(s)
- Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma Sapienza and Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, I-56127 Pisa, Italy
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9
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Zhang XF, He YC, Eggert S, Moessner R, Pollmann F. Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice. PHYSICAL REVIEW LETTERS 2018; 120:115702. [PMID: 29601746 DOI: 10.1103/physrevlett.120.115702] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Revised: 12/29/2017] [Indexed: 06/08/2023]
Abstract
We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.
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Affiliation(s)
- Xue-Feng Zhang
- Department of Physics, Chongqing University, Chongqing 401331, People's Republic of China
- Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Yin-Chen He
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Sebastian Eggert
- Physics Department and Research Center OPTIMAS, University of Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Roderich Moessner
- Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Frank Pollmann
- Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Department of Physics, Technical University of Munich, 85748 Garching, Germany
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10
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Sato T, Hohenadler M, Assaad FF. Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry. PHYSICAL REVIEW LETTERS 2017; 119:197203. [PMID: 29219508 DOI: 10.1103/physrevlett.119.197203] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Indexed: 06/07/2023]
Abstract
We consider a model of Dirac fermions in 2+1 dimensions with dynamically generated, anticommuting SO(3) Néel and Z_{2} Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z_{3} vortices in the Kekulé mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which the Néel, Kekulé, and semimetallic phases meet. The present sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.
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Affiliation(s)
- Toshihiro Sato
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Fakher F Assaad
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
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11
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Li ZX, Jiang YF, Jian SK, Yao H. Fermion-induced quantum critical points. Nat Commun 2017; 8:314. [PMID: 28827582 PMCID: PMC5566446 DOI: 10.1038/s41467-017-00167-6] [Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2017] [Accepted: 06/07/2017] [Indexed: 12/04/2022] Open
Abstract
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.
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Affiliation(s)
- Zi-Xiang Li
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Yi-Fan Jiang
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Shao-Kai Jian
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China.
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing, 100084, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China.
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12
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Upadhyay SK, Iyer KK, Gohil S, Ghosh S, Paulose PL, Sampathkumaran EV. Pyrocurrent anomalies and intrinsic magnetodielectric behavior near room temperature in Li 2Ni 2Mo 3O 12, a compound with distorted honeycomb and spin-chains. Sci Rep 2017; 7:4449. [PMID: 28667268 PMCID: PMC5493632 DOI: 10.1038/s41598-017-04025-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Accepted: 05/08/2017] [Indexed: 11/09/2022] Open
Abstract
Keeping current interests to identify materials with intrinsic magnetodielectric behaviour near room temperature and with novel pyroelectric current anomalies, we report temperature and magnetic-field dependent behavior of complex dielectric permittivity and pyroelectric current for an oxide, Li2Ni2Mo3O12, containing magnetic ions with (distorted) honey-comb and chain arrangement and ordering magnetically below 8 K. The dielectric data reveal the existence of relaxor ferroelectricity behaviour in the range 160-240 K and there are corresponding Raman mode anomalies as well in this temperature range. Pyrocurrent behavior is also consistent with this interpretation, with the pyrocurrent peak-temperature interestingly correlating with the poling temperature. 7Li NMR offer an evidence for crystallographic disorder intrinsic to this compound and we therefore conclude that such a disorder is apparently responsible for the randomness of local electric field leading to relaxor ferroelectric property. Another observation of emphasis is that there is a notable decrease in the dielectric constant with the application of magnetic field to the tune of about -2.4% at 300 K, with the magnitude varying marginally with temperature. Small loss factor values validate the intrinsic behaviour of the magnetodielectric effect at room temperature.
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Affiliation(s)
- Sanjay Kumar Upadhyay
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India
| | - Kartik K Iyer
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India
| | - Smita Gohil
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India
| | - Shankar Ghosh
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India
| | - P L Paulose
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India
| | - E V Sampathkumaran
- Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India.
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13
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Huerga D, Greco A, Gazza C, Muramatsu A. Translation-Invariant Parent Hamiltonians of Valence Bond Crystals. PHYSICAL REVIEW LETTERS 2017; 118:167202. [PMID: 28474946 DOI: 10.1103/physrevlett.118.167202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Indexed: 06/07/2023]
Abstract
We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S=1/2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.
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Affiliation(s)
- Daniel Huerga
- Institut für Theoretische Physik III, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
| | - Andrés Greco
- Instituto de Física Rosario, CONICET, and Facultad de Ciencias Exactas Ingeniería y Agrimensura, Universidad Nacional de Rosario, Boulevard 27 de Febrero 210 bis, 2000 Rosario, Argentina
| | - Claudio Gazza
- Instituto de Física Rosario, CONICET, and Facultad de Ciencias Exactas Ingeniería y Agrimensura, Universidad Nacional de Rosario, Boulevard 27 de Febrero 210 bis, 2000 Rosario, Argentina
| | - Alejandro Muramatsu
- Institut für Theoretische Physik III, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
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14
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Ghorbani E, Shahbazi F, Mosadeq H. Quantum phase diagram of distorted J 1 - J 2 Heisenberg S = 1/2 antiferromagnet in honeycomb lattice: a modified spin wave study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:406001. [PMID: 27518832 DOI: 10.1088/0953-8984/28/40/406001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using the modified spin wave method, we study the [Formula: see text] Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter [Formula: see text]: (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for [Formula: see text], (2) a magnetically gapped disordered state for [Formula: see text], preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for [Formula: see text]. We also explore the phase diagram of a distorted [Formula: see text] model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model.
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Affiliation(s)
- Elaheh Ghorbani
- Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran
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15
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Nakayama Y, Ohtsuki T. Necessary Condition for Emergent Symmetry from the Conformal Bootstrap. PHYSICAL REVIEW LETTERS 2016; 117:131601. [PMID: 27715104 DOI: 10.1103/physrevlett.117.131601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Indexed: 06/06/2023]
Abstract
We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Z_{n}) to continuous symmetry [e.g., U(1)] under the renormalization group flow. In three dimensions, in order for Z_{2} symmetry to be enhanced to U(1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ_{1}>1.08. We also obtain the similar necessary conditions for Z_{3} symmetry with Δ_{1}>0.580 and Z_{4} symmetry with Δ_{1}>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O(n) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.
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Affiliation(s)
- Yu Nakayama
- Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
| | - Tomoki Ohtsuki
- Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
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Zvereva EA, Stratan MI, Ushakov AV, Nalbandyan VB, Shukaev IL, Silhanek AV, Abdel-Hafiez M, Streltsov SV, Vasiliev AN. Orbitally induced hierarchy of exchange interactions in the zigzag antiferromagnetic state of honeycomb silver delafossite Ag3Co2SbO6. Dalton Trans 2016; 45:7373-84. [PMID: 27029886 DOI: 10.1039/c6dt00516k] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with Néel temperature TN ∼ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-flop type) transition below TN in moderate magnetic fields. The GGA+U calculations show the importance of the orbital degrees of freedom, which maintain a hierarchy of exchange interaction in the system. The strongest antiferromagnetic exchange coupling was found in the shortest Co-Co pairs and is due to direct and superexchange interaction between the half-filled xz + yz orbitals pointing directly to each other. The other four out of six nearest neighbor exchanges within the cobalt hexagon are suppressed, since for these bonds the active half-filled orbitals turned out to be parallel and do not overlap. The electron spin resonance (ESR) spectra reveal a broad absorption line attributed to the Co(2+) ion in an octahedral coordination with an average effective g-factor g = 2.40 ± 0.05 at room temperature and show strong divergence of the ESR parameters below ∼150 K, which implies an extended region of short-range correlations. Based on the results of magnetic and thermodynamic studies in applied fields, we propose a magnetic phase diagram for the new honeycomb-lattice delafossite.
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Affiliation(s)
- E A Zvereva
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia.
| | - M I Stratan
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia.
| | - A V Ushakov
- Institute of Metal Physics, S. Kovalevskoy St. 18, 620990 Ekaterinburg, Russia
| | - V B Nalbandyan
- Chemistry Faculty, Southern Federal University, 344090 Rostov-on-Don, Russia
| | - I L Shukaev
- Chemistry Faculty, Southern Federal University, 344090 Rostov-on-Don, Russia
| | - A V Silhanek
- Département de Physique, Université de Liége, B-4000 Sart Tilman, Belgium
| | - M Abdel-Hafiez
- Institute of Physics, Goethe University Frankfurt, 60438 Frankfurt/M, Germany and Faculty of Science, Physics Department, Fayoum University, 63514 Fayoum, Egypt and Center for High Pressure Science & Technology Advanced Research, 1690 Cailun Rd, Shanghai, 201203, P.R. China
| | - S V Streltsov
- Institute of Metal Physics, S. Kovalevskoy St. 18, 620990 Ekaterinburg, Russia and Ural Federal University, 620002 Ekaterinburg, Russia
| | - A N Vasiliev
- Faculty of Physics, Moscow State University, 119991 Moscow, Russia. and Ural Federal University, 620002 Ekaterinburg, Russia and National University of Science and Technology "MISiS", 119049 Moscow, Russia
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Harada K. Kernel method for corrections to scaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012106. [PMID: 26274124 DOI: 10.1103/physreve.92.012106] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Indexed: 06/04/2023]
Abstract
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.
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Affiliation(s)
- Kenji Harada
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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Gong SS, Zhu W, Sheng DN, Motrunich OI, Fisher MPA. Plaquette ordered phase and quantum phase diagram in the spin-1/2 J(1)-J(2) square Heisenberg model. PHYSICAL REVIEW LETTERS 2014; 113:027201. [PMID: 25062223 DOI: 10.1103/physrevlett.113.027201] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2014] [Indexed: 06/03/2023]
Abstract
We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.
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Affiliation(s)
- Shou-Shu Gong
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Wei Zhu
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Olexei I Motrunich
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Matthew P A Fisher
- Department of Physics, University of California, Santa Barbara, California 93106-9530, USA
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Huh Y, Strack P, Sachdev S. Vector boson excitations near deconfined quantum critical points. PHYSICAL REVIEW LETTERS 2013; 111:166401. [PMID: 24182284 DOI: 10.1103/physrevlett.111.166401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2013] [Indexed: 06/02/2023]
Abstract
We show that the Néel states of two-dimensional antiferromagnets have low energy vector boson excitations in the vicinity of deconfined quantum critical points. We compute the universal damping of these excitations arising from spin-wave emission. Detection of such a vector boson will demonstrate the existence of emergent topological gauge excitations in a quantum spin system.
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Affiliation(s)
- Yejin Huh
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Block MS, Melko RG, Kaul RK. Fate of CPN-1 fixed points with q monopoles. PHYSICAL REVIEW LETTERS 2013; 111:137202. [PMID: 24116811 DOI: 10.1103/physrevlett.111.137202] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2013] [Indexed: 06/02/2023]
Abstract
We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.
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Affiliation(s)
- Matthew S Block
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA
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