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Fontenele RA, Dos Anjos Sousa Júnior S, Cysne TP, Costa NC. The impact of Rashba spin-orbit coupling in charge-ordered systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:225601. [PMID: 38394686 DOI: 10.1088/1361-648x/ad2cc9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 02/23/2024] [Indexed: 02/25/2024]
Abstract
We study the impact of the Rashba spin-orbit coupling (RSOC) on the stability of charge-density wave (CDW) in systems with large electron-phonon coupling (EPC). Here, the EPC is considered in the framework of the Holstein model at the half-filled square lattice. We obtain the phase diagram of the Rashba-Holstein model using the Hartree-Fock mean-field theory, and identify the boundaries of the CDW and Rashba metal phases. We notice that the RSOC disfavors the CDW phase, driving the system to a correlated Rashba metal. Also, we employ a cluster perturbation theory (CPT) approach to investigate the phase diagram beyond the Hartree-Fock approximation. The quantum correlations captured by CPT indicate that the RSOC is even more detrimental to CDW than previously anticipated. That is, the Rashba metal region is observed to be expanded in comparison to the mean-field case. Additionally, we investigate pairing correlations, and the results further strengthen the identification of critical points.
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Affiliation(s)
- Rodrigo A Fontenele
- Instituto de Física, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro, RJ, Brazil
| | | | - Tarik P Cysne
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, RJ, Brazil
| | - Natanael C Costa
- Instituto de Física, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro, RJ, Brazil
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2
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Yang ZK, Pan XY, Liu GZ. A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:075601. [PMID: 36541489 DOI: 10.1088/1361-648x/aca948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 12/06/2022] [Indexed: 06/17/2023]
Abstract
In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger (DS) integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the DS equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.
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Affiliation(s)
- Zhao-Kun Yang
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Xiao-Yin Pan
- Department of Physics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | - Guo-Zhu Liu
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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3
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Tabatabaei SM, Negari AR, Maciejko J, Vaezi A. Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum Monte Carlo Study. PHYSICAL REVIEW LETTERS 2022; 128:225701. [PMID: 35714234 DOI: 10.1103/physrevlett.128.225701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with N=2 spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength U_{c}=7.28±0.02 in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding N=2 chiral Ising Gross-Neveu universality class: the inverse correlation length exponent ν^{-1}=1.19±0.03, the order parameter anomalous dimension η_{ϕ}=0.31±0.01, and the fermion anomalous dimension η_{ψ}=0.136±0.005.
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Affiliation(s)
- S Mojtaba Tabatabaei
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Amir-Reza Negari
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Joseph Maciejko
- Department of Physics & Theoretical Physics Institute (TPI), University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - Abolhassan Vaezi
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
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4
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Cohen-Stead B, Bradley O, Miles C, Batrouni G, Scalettar R, Barros K. Fast and scalable quantum Monte Carlo simulations of electron-phonon models. Phys Rev E 2022; 105:065302. [PMID: 35854479 DOI: 10.1103/physreve.105.065302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.
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Affiliation(s)
| | - Owen Bradley
- Department of Physics, University of California, Davis, California 95616, USA
| | - Cole Miles
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - George Batrouni
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, (INPHYNI), 06103 Nice, France
- Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore
| | - Richard Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - Kipton Barros
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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5
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Weber M, Freericks JK. Real-time evolution of static electron-phonon models in time-dependent electric fields. Phys Rev E 2022; 105:025301. [PMID: 35291073 DOI: 10.1103/physreve.105.025301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of 162 sites (in one dimension) or 16×16 square lattices (in two dimensions).
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Affiliation(s)
- Manuel Weber
- Department of Physics, Georgetown University, Washington, DC 20057, USA
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - James K Freericks
- Department of Physics, Georgetown University, Washington, DC 20057, USA
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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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Yao M, Wang D, Wang QH. Reducing autocorrelation time in determinant quantum Monte Carlo using the Wang-Landau algorithm: Application to the Holstein model. Phys Rev E 2021; 104:025305. [PMID: 34525639 DOI: 10.1103/physreve.104.025305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 07/29/2021] [Indexed: 11/07/2022]
Abstract
When performing a Monte Carlo calculation, the running time should, in principle, be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this paper, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space," which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and honeycomb lattices. Based on such a Wang-Landau assisted determinant quantum Monte Carlo method, some models with long autocorrelation times can now be simulated possibly.
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Affiliation(s)
- Meng Yao
- National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing, 210093, China
| | - Da Wang
- National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing, 210093, China.,Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Qiang-Hua Wang
- National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing, 210093, China.,Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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Costa NC, Seki K, Sorella S. Magnetism and Charge Order in the Honeycomb Lattice. PHYSICAL REVIEW LETTERS 2021; 126:107205. [PMID: 33784139 DOI: 10.1103/physrevlett.126.107205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2020] [Accepted: 02/15/2021] [Indexed: 06/12/2023]
Abstract
Despite being relevant to better understand the properties of honeycomblike systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on interacting Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings provide quantitative and qualitative descriptions of the model at intermediate coupling strengths, and may shed light on the emergence of many-body properties in honeycomblike systems.
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Affiliation(s)
- Natanael C Costa
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Instituto de Física, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro RJ, Brazil
| | - Kazuhiro Seki
- Computational Quantum Matter Research Team, RIKEN, Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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Xing B, Chiu WT, Poletti D, Scalettar RT, Batrouni G. Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model. PHYSICAL REVIEW LETTERS 2021; 126:017601. [PMID: 33480778 DOI: 10.1103/physrevlett.126.017601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
Over the past several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, show that a bond ordered wave (BOW) insulator is present in the ground state at half filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of Z_{4} symmetry.
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Affiliation(s)
- Bo Xing
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Wei-Ting Chiu
- Department of Physics, University of California, Davis, California 95616, USA
| | - Dario Poletti
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - George Batrouni
- Université Côte d'Azur, INPHYNI, CNRS, 0600 Nice, France
- Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore
- Beijing Computational Science Research Center, Beijing 100193, China
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Xu XY, Hong Liu Z, Pan G, Qi Y, Sun K, Meng ZY. Revealing fermionic quantum criticality from new Monte Carlo techniques. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:463001. [PMID: 31425147 DOI: 10.1088/1361-648x/ab3295] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications, and partially awakened by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems face the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc, where signatures of fermionic quantum criticality exist.
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Affiliation(s)
- Xiao Yan Xu
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, People's Republic of China
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Chen C, Xu XY, Meng ZY, Hohenadler M. Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons. PHYSICAL REVIEW LETTERS 2019; 122:077601. [PMID: 30848656 DOI: 10.1103/physrevlett.122.077601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/09/2023]
Abstract
The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.
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Affiliation(s)
- Chuang Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Xiao Yan Xu
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Zi Yang Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center of Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
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