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Wang X, Zhu W. A microscopic view of checkerboard and striped charge orders through doping antiferromagnetic Mott insulator. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:265602. [PMID: 38518372 DOI: 10.1088/1361-648x/ad3709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 03/22/2024] [Indexed: 03/24/2024]
Abstract
The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of thes-dexchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.
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Affiliation(s)
- Xuanlan Wang
- Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Wei Zhu
- Key Laboratory for Quantum Materials of Zhejiang Province, School of Science, Westlake University, Hangzhou 310024, People's Republic of China
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2
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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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3
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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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Wang Y, Chen Z, Shi T, Moritz B, Shen ZX, Devereaux TP. Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates. PHYSICAL REVIEW LETTERS 2021; 127:197003. [PMID: 34797146 DOI: 10.1103/physrevlett.127.197003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 09/22/2021] [Indexed: 06/13/2023]
Abstract
Establishing a minimal microscopic model for cuprates is a key step towards the elucidation of a high-T_{c} mechanism. By a quantitative comparison with a recent in situ angle-resolved photoemission spectroscopy measurement in doped 1D cuprate chains, our simulation identifies a crucial contribution from long-range electron-phonon coupling beyond standard Hubbard models. Using reasonable ranges of coupling strengths and phonon energies, we obtain a strong attractive interaction between neighboring electrons, whose strength is comparable to experimental observations. Nonlocal couplings play a significant role in the mediation of neighboring interactions. Considering the structural and chemical similarity between 1D and 2D cuprate materials, this minimal model with long-range electron-phonon coupling will provide important new insights on cuprate high-T_{c} superconductivity and related quantum phases.
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Affiliation(s)
- Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Zhuoyu Chen
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Tao Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Brian Moritz
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Zhi-Xun Shen
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Thomas P Devereaux
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
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Nakamura K, Tanimura Y. Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach. J Chem Phys 2021; 155:064106. [PMID: 34391366 DOI: 10.1063/5.0060208] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that arises from the environment becomes significant. We therefore include heat baths with infinite heat capacity in the model to introduce thermal effects characterized by fluctuation and dissipation to the system dynamics. By reducing the number of degrees of freedom of the heat baths, we derive numerically "exact" hierarchical equations of motion for the reduced density matrix of the HH system. As demonstrations, we calculate the optical response of the system in two- and four-site cases under external electric fields. The results indicate that the effective strength of the system-bath coupling becomes large as the number of sites increases. Excitation of electrons promotes the conductivity when the Coulomb repulsion is equivalent to or dominates the electron-phonon coupling, whereas excitation of optical vibrations always suppresses the conductivity.
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Affiliation(s)
- Kiyoto Nakamura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan
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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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Han Z, Kivelson SA, Yao H. Strong Coupling Limit of the Holstein-Hubbard Model. PHYSICAL REVIEW LETTERS 2020; 125:167001. [PMID: 33124862 DOI: 10.1103/physrevlett.125.167001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 09/15/2020] [Indexed: 06/11/2023]
Abstract
We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong coupling expansion. We find all sorts of interesting phases including a pair-density wave, a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave, spin-density-wave, and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e., the ratio of characteristic phonon frequency to the strength of interactions.
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Affiliation(s)
- Zhaoyu Han
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Steven A Kivelson
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Hong Yao
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Institute of Advanced Study, Tsinghua University, Beijing 100084, China
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Costa NC, Blommel T, Chiu WT, Batrouni G, Scalettar RT. Phonon Dispersion and the Competition between Pairing and Charge Order. PHYSICAL REVIEW LETTERS 2018; 120:187003. [PMID: 29775370 DOI: 10.1103/physrevlett.120.187003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Indexed: 06/08/2023]
Abstract
The Holstein model describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge-density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature T_{cdw} for CDW order and also uncover several novel features of diagonal long-range order in the phase diagram, including a competition between charge patterns at momenta q=(π,π) and q=(0,π) which lends insight into the relationship between Fermi surface nesting and the wave vector at which charge order occurs. We also demonstrate SC order at half filling in situations where a nonzero bandwidth sufficiently suppresses T_{cdw}.
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Affiliation(s)
- N C Costa
- Instituto de Física, Universidade Federal do Rio de Janeiro, Cx.P. 68.528, 21941-972 Rio de Janeiro RJ, Brazil
- Department of Physics, University of California, Davis, California 95616, USA
| | - T Blommel
- Department of Physics, University of California, Davis, California 95616, USA
- Department of Physics, North Dakota State University, Fargo, North Dakota 58105, USA
| | - W-T Chiu
- Department of Physics, University of California, Davis, California 95616, USA
| | - G Batrouni
- Université Côte d'Azur, INPHYNI, CNRS, 0600 Nice, France
- Beijing Computational Science Research Center, Beijing 100193, China
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
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