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Ge ZY, Zhang YR, Nori F. Nonmesonic Quantum Many-Body Scars in a 1D Lattice Gauge Theory. PHYSICAL REVIEW LETTERS 2024; 132:230403. [PMID: 38905688 DOI: 10.1103/physrevlett.132.230403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Revised: 05/02/2024] [Accepted: 05/06/2024] [Indexed: 06/23/2024]
Abstract
We investigate the meson excitations (particle-antiparticle bound states) in quantum many-body scars of a 1D Z_{2} lattice gauge theory coupled to a dynamical spin-1/2 chain as a matter field. By introducing a string representation of the physical Hilbert space, we express a scar state |Ψ_{n,l}⟩ as a superposition of all string bases with an identical string number n and a total length l. For the small-l scar state |Ψ_{n,l}⟩, the gauge-invariant spin exchange correlation function of the matter field hosts an exponential decay as the distance increases, indicating the existence of stable mesons. However, for large l, the correlation function exhibits a power-law decay, signaling the emergence of nonmesonic excitations. Furthermore, we show that this mesonic-nonmesonic crossover can be detected by the quench dynamics, starting from two low-entangled initial states, respectively, which are experimentally feasible in quantum simulators. Our results expand the physics of quantum many-body scars in lattice gauge theories and reveal that the nonmesonic state can also manifest ergodicity breaking.
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Affiliation(s)
- Zi-Yong Ge
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - Yu-Ran Zhang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Quantum Information Physics Theory Research Team, Center for Quantum Computing, RIKEN, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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2
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Müller T, Kiese D, Niggemann N, Sbierski B, Reuther J, Trebst S, Thomale R, Iqbal Y. Pseudo-fermion functional renormalization group for spin models. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:036501. [PMID: 38241725 DOI: 10.1088/1361-6633/ad208c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Accepted: 01/19/2024] [Indexed: 01/21/2024]
Abstract
For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow ofm-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.
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Affiliation(s)
- Tobias Müller
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg D-97074, Germany
| | - Dominik Kiese
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, United States of America
| | - Nils Niggemann
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, D-14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
- Department of Physics and Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), Indian Institute of Technology Madras, Chennai 600036, India
| | - Björn Sbierski
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstraße 37, München D-80333, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Johannes Reuther
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, D-14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
- Department of Physics and Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), Indian Institute of Technology Madras, Chennai 600036, India
| | - Simon Trebst
- Institut für Theoretische Physik, Zülpicher Straße 77a, Universität zu Köln, 50937 Köln, Germany
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg D-97074, Germany
- Department of Physics and Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), Indian Institute of Technology Madras, Chennai 600036, India
| | - Yasir Iqbal
- Department of Physics and Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), Indian Institute of Technology Madras, Chennai 600036, India
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Christos M, Luo ZX, Shackleton H, Zhang YH, Scheurer MS, Sachdev S. A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice. Proc Natl Acad Sci U S A 2023; 120:e2302701120. [PMID: 37192166 PMCID: PMC10214163 DOI: 10.1073/pnas.2302701120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 04/15/2023] [Indexed: 05/18/2023] Open
Abstract
We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.
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Affiliation(s)
- Maine Christos
- Department of Physics, Harvard University, Cambridge, MA02138
| | - Zhu-Xi Luo
- Department of Physics, Harvard University, Cambridge, MA02138
| | - Henry Shackleton
- Department of Physics, Harvard University, Cambridge, MA02138
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY10010
| | - Ya-Hui Zhang
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD21218
| | - Mathias S. Scheurer
- Institute for Theoretical Physics, University of Innsbruck, InnsbruckA-6020, Austria
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA02138
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Jiang YF, Yao H, Yang F. Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:187003. [PMID: 34767423 DOI: 10.1103/physrevlett.127.187003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 05/22/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this Letter, we propose a new class of variational states for this model and perform a large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field Ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2×2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasiparticles. We further study experimentally relevant properties of this intriguing pairing state.
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Affiliation(s)
- Yi-Fan Jiang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Hong Yao
- Institute of Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Fan Yang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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Nataf P, Lajkó M, Wietek A, Penc K, Mila F, Läuchli AM. Chiral Spin Liquids in Triangular-Lattice SU(N) Fermionic Mott Insulators with Artificial Gauge Fields. PHYSICAL REVIEW LETTERS 2016; 117:167202. [PMID: 27792381 DOI: 10.1103/physrevlett.117.167202] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/06/2023]
Abstract
We show that, in the presence of a π/2 artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU(N) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of N low-lying singlets for periodic boundary conditions, and by chiral edge states described by the SU(N)_{1} Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for N between 3 and 9, and by a parton construction based on a set of N Gutzwiller projected fermionic wave functions with flux π/N per triangular plaquette. Experimental implications are briefly discussed.
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Affiliation(s)
- Pierre Nataf
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Miklós Lajkó
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Alexander Wietek
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Karlo Penc
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest, P.O.B. 49, Hungary
- MTA-BME Lendület Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary
| | - Frédéric Mila
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Andreas M Läuchli
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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6
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Mezzacapo A, Rico E, Sabín C, Egusquiza IL, Lamata L, Solano E. Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits. PHYSICAL REVIEW LETTERS 2015; 115:240502. [PMID: 26705616 DOI: 10.1103/physrevlett.115.240502] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Indexed: 06/05/2023]
Abstract
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.
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Affiliation(s)
- A Mezzacapo
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - E Rico
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
| | - C Sabín
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - I L Egusquiza
- Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - L Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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7
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Abstract
Abstract
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new ‘topological’ phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase—topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).
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Affiliation(s)
- Xiao-Gang Wen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
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Fukushima T, Katayama-Yoshida H, Uede H, Takawashi Y, Nakanishi A, Sato K. Computational materials design of negative effective U system in hole-doped chalcopyrite CuFeS2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:355502. [PMID: 25109352 DOI: 10.1088/0953-8984/26/35/355502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
A general rule of negative effective U(U(eff)) system caused by (i) exchange correlation and (ii) charge excitation mechanisms is proposed. Based on the general rule, we perform ab initio electronic structure calculations by generalized gradient approximation (GGA) + U method for hole-doped chalcopyrite CuFeS2 [Cu(+)(d(10))Fe(3+)(d(5))S(2-)(s(2)p(6))2]. It is found from our calculations that the hole-doped CuFeS2 has the negative U(eff) = -0.44 eV, where U(eff) ≡ E(N + 1) + E(N - 1) - 2E(N) < 0 and E(N) is the total energy of the hole-doped CuFeS2. The negative U(eff) is caused by the charge-excitation in the hole-doped Cu(2+)(d(9)) and S(-)(s(2)p(5)), and also caused by the exchange-correlation in the hole-doped Fe(4+)(d(4)). The strong attractive electron-electron interaction (U(eff) = -0.44 eV ∼ -5000 K) originates from the purely electronic mechanism. The closed shell of the d(10) electronic configuration is more stable than the d(9) electronic configuration, since the first excited state with the d(9)s(1) electronic configuration and the ground state with the d(10) electronic configuration are very close, then these two states repel very strongly through the second order perturbation. Therefore, the spin-polarized total energy curve for the hole-doped CuFeS2 shows the strong upward convexity with N - 1, N and N + 1 electronic configurations leading to the negative U(eff). The hole-doped paramagnetic and metallic CuFeS2 with the negative U(eff) may cause a possible high-Tc superconductor (Tc ∼ 1000 K, if 2Δ/kBTc ≈ 10 by assuming a strong coupling regime) because of the strong attractive electron-electron interactions (superconducting gap Δ ≈ |U(eff|) ∼ 5000 K). Finally, we propose a new computational materials design methodology to design ultra high-Tc superconductors by using three steps starting from the atomic number only.
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Affiliation(s)
- T Fukushima
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
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Hayward LE, Hawthorn DG, Melko RG, Sachdev S. Angular fluctuations of a multicomponent order describe the pseudogap of YBa2Cu3O(6+x). Science 2014; 343:1336-9. [PMID: 24653030 DOI: 10.1126/science.1246310] [Citation(s) in RCA: 95] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The hole-doped cuprate high-temperature superconductors enter the pseudogap regime as their superconducting critical temperature, Tc, falls with decreasing hole density. Recent x-ray scattering experiments in YBa2Cu3O(6+x) observe incommensurate charge-density wave fluctuations whose strength rises gradually over a wide temperature range above Tc, but then decreases as the temperature is lowered below Tc. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a six-dimensional space. The theory provides a natural quantitative fit to the x-ray data and can be a basis for understanding other characteristics of the pseudogap.
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Affiliation(s)
- Lauren E Hayward
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Sachdev S, La Placa R. Bond order in two-dimensional metals with antiferromagnetic exchange interactions. PHYSICAL REVIEW LETTERS 2013; 111:027202. [PMID: 23889434 DOI: 10.1103/physrevlett.111.027202] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2013] [Indexed: 06/02/2023]
Abstract
We present an unrestricted Hartree-Fock computation of charge-ordering instabilities of two-dimensional metals with antiferromagnetic exchange interactions, allowing for arbitrary ordering wave vectors and internal wave functions of the particle-hole pair condensate. We find that the ordering has a dominant d symmetry of rotations about lattice points for a range of ordering wave vectors, including those observed in recent experiments at low temperatures on YBa2Cu3O(y). This d symmetry implies the charge ordering is primarily on the bonds of the Cu lattice, and we propose incommensurate bond order parameters for the underdoped cuprates. The field theory for the onset of Néel order in a metal has an emergent pseudospin symmetry which "rotates" d-wave Cooper pairs to particle-hole pairs [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)]; our results show that this symmetry has consequences even when the spin correlations are short ranged and incommensurate.
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Affiliation(s)
- Subir Sachdev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Kim KS, Kim HC. A phenomenological description of an incoherent Fermi liquid near optimal doping in high Tc cuprates. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:495701. [PMID: 22101360 DOI: 10.1088/0953-8984/23/49/495701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Marginal Fermi-liquid physics near optimal doping in high T(c) cuprates has been explained within two competing scenarios such as the spin-fluctuation theory based on an itinerant picture and the slave-particle approach based on a localized picture. In this study we propose an alternative scenario for the anomalous transport within the context of the slave-particle approach. Although the marginal Fermi-liquid phenomenology was interpreted previously within deconfinement of the compact gauge theory, referred to as the strange metal phase, we start from confinement, introducing the Polyakov loop parameter into an SU(2) gauge theory formulation of the t-J model. The Polyakov loop parameter gives rise to incoherent electrons through the confinement of spinons and holons, which result from huge imaginary parts of self-energy corrections for spinons and holons. This confinement scenario serves a novel mechanism for the marginal Fermi-liquid transport in the respect that the scattering source has nothing to do with symmetry breaking. Furthermore, the incoherent Fermi-liquid state evolves into the Fermi-liquid phase through crossover instead of an artificial second-order transition as temperature is lowered, where the crossover phenomenon does not result from the Anderson-Higgs mechanism but originates from an energy scale in the holon sector. We fit experimental data for the electrical resistivity around the optimal doping and find a reasonable match between our theory and the experiment.
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Affiliation(s)
- Ki-Seok Kim
- Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790-784, Korea.
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12
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Ran Y, Wen XG. Detecting topological order through a continuous quantum phase transition. PHYSICAL REVIEW LETTERS 2006; 96:026802. [PMID: 16486612 DOI: 10.1103/physrevlett.96.026802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2005] [Indexed: 05/06/2023]
Abstract
We study a continuous quantum phase transition that breaks a Z2 symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well-defined symmetry-breaking order parameter. The new critical point arises since the transition not only breaks the Z2 symmetry, it also changes the topological or quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological or quantum orders in those phases.
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Affiliation(s)
- Ying Ran
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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13
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Lee DH. Superconductivity in a doped mott insulator. PHYSICAL REVIEW LETTERS 2000; 84:2694-2697. [PMID: 11017302 DOI: 10.1103/physrevlett.84.2694] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/1999] [Indexed: 05/23/2023]
Abstract
Starting from the d-wave resonating-valence-bond mean-field theory of Kotliar and Liu, we present a new, long-wavelength/low-energy exact, treatment of gauge fluctuations. The result is a theory of gapless fermion quasiparticles coupled to superconducting phase fluctuations. We will discuss the physical implications, and the similarity and differences to a theory of superconductors with phase fluctuations.
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Affiliation(s)
- DH Lee
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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14
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15
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Ng TK. Vortices in Schwinger-Boson mean-field theory of two-dimensional quantum antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9491-9499. [PMID: 9979997 DOI: 10.1103/physrevb.52.9491] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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16
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Mudry C, Fradkin E. Mechanism of spin and charge separation in one-dimensional quantum antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:11409-11428. [PMID: 9975272 DOI: 10.1103/physrevb.50.11409] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Mudry C, Fradkin E. Separation of spin and charge quantum numbers in strongly correlated systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:5200-5219. [PMID: 10011471 DOI: 10.1103/physrevb.49.5200] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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18
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Khveshchenko DV. Exact and broken symmetries in a hydrodynamical description of chiral spin states. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:15926-15932. [PMID: 10008152 DOI: 10.1103/physrevb.48.15926] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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19
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Luo XQ, Chen QZ. Vacuum structure and chiral-symmetry breaking in (2+1)-dimensional lattice gauge theories with fermions. Int J Clin Exp Med 1992; 46:814-823. [PMID: 10014992 DOI: 10.1103/physrevd.46.814] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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20
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Goff WE, Walker MB. Mean-field states in an itinerant Heisenberg model. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:12905-12910. [PMID: 10001353 DOI: 10.1103/physrevb.45.12905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Tomboulis ET. Nonexistence of chiral spin states in frustrated antiferromagnets. PHYSICAL REVIEW LETTERS 1992; 68:3100-3103. [PMID: 10045607 DOI: 10.1103/physrevlett.68.3100] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ye J, Sachdev S. Superconducting, metallic, and insulating phases in a model of CuO2 layers. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:10173-10189. [PMID: 9999022 DOI: 10.1103/physrevb.44.10173] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG. Mean-field theory of spin-liquid states with finite energy gap and topological orders. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:2664-2672. [PMID: 9999836 DOI: 10.1103/physrevb.44.2664] [Citation(s) in RCA: 88] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Balatsky A, Kalmeyer V. Singlet-pair superconductivity in the two-component anyon gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:6228-6231. [PMID: 9998046 DOI: 10.1103/physrevb.43.6228] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Wen XG. Non-Abelian statistics in the fractional quantum Hall states. PHYSICAL REVIEW LETTERS 1991; 66:802-805. [PMID: 10043904 DOI: 10.1103/physrevlett.66.802] [Citation(s) in RCA: 58] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Dagotto E, Joynt R, Moreo A, Bacci S, Gagliano E. Strongly correlated electronic systems with one hole: Dynamical properties. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:9049-9073. [PMID: 9993249 DOI: 10.1103/physrevb.41.9049] [Citation(s) in RCA: 135] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Appelquist T, Nash D. Critical behavior in (2+1)-dimensional QCD. PHYSICAL REVIEW LETTERS 1990; 64:721-724. [PMID: 10042061 DOI: 10.1103/physrevlett.64.721] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Wen XG, Wilczek F, Zee A. Chiral spin states and superconductivity. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:11413-11423. [PMID: 9947970 DOI: 10.1103/physrevb.39.11413] [Citation(s) in RCA: 443] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Dagotto E, Kogut JB, Kocic A. Computer simulation of chiral-symmetry breaking in (2+1)-dimensional QED with N flavors. PHYSICAL REVIEW LETTERS 1989; 62:1083-1086. [PMID: 10039572 DOI: 10.1103/physrevlett.62.1083] [Citation(s) in RCA: 33] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Andrei N, Coleman P. Cooper instability in the presence of a spin liquid. PHYSICAL REVIEW LETTERS 1989; 62:595-598. [PMID: 10040275 DOI: 10.1103/physrevlett.62.595] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Annett JF, Goldenfeld N, Renn SR. Order parameters in the resonating-valence-bond model. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:708-710. [PMID: 9947207 DOI: 10.1103/physrevb.39.708] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Dombre T, Kotliar G. Instability of the long-range resonating-valence-bond state in the mean-field approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:855-857. [PMID: 9947250 DOI: 10.1103/physrevb.39.855] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG. Charge-e bosons, neutral fermions, and h/2e flux-field theory models. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:12004-12007. [PMID: 9946126 DOI: 10.1103/physrevb.38.12004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Marston JB. U(1) gauge theory of the Heisenberg antiferromagnet. PHYSICAL REVIEW LETTERS 1988; 61:1914-1917. [PMID: 10038931 DOI: 10.1103/physrevlett.61.1914] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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