Variational Monte Carlo method for electron-phonon coupled systems

Ohgoe, Takahiro; Imada, Masatoshi

doi:10.1103/physrevb.89.195139

Cited by 27 publications

(35 citation statements)

References 66 publications

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“…Applications of the t-VMC method to such models are intriguing future issues. Furthermore, the VMC method can be applied not only to purely electronic systems but also to electron-phonon coupled systems 66 . Therefore, it would be possible to study the phenomena of relaxation process and photoinduced phase transitions through phonon modes in real materials such as copper oxides.…”

Section: Discussionmentioning

confidence: 99%

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

2015

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We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a time-dependent trial wave function with many variational parameters, which is suitable for nonequilibrium strongly correlated electron systems. As the trial state, we adopt the generalized pair-product wave function with correlation factors and quantum-number projections. This trial wave function has been proven to accurately describe ground states of strongly correlated electron systems. To show the accuracy and efficiency of our trial wave function in nonequilibrium states as well, we present our benchmark results for relaxation dynamics during and after interaction quench protocols of fermionic Hubbard models. We find that our trial wave function well reproduces the exact results for the time evolution of physical quantities such as energy, momentum distribution, spin structure factor, and superconducting correlations. These results show that the t-VMC with our trial wave function offers an efficient and accurate way to study challenging problems of nonequilibrium dynamics in strongly correlated electron systems.

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Section: Discussionmentioning

confidence: 99%

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

2015

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“…A variety of different quantum Monte Carlo methods have been developed to investigate the Holstein model [26,39,[46][47][48][49][50][51]. For wave-function based methods, such as exact diagonalization (ED) or the densitymatrix renormalization group (DMRG), electron-phonon systems are computationally very demanding.…”

Section: Introductionmentioning

confidence: 99%

Charge-density-wave melting in the one-dimensional Holstein model

et al. 2020

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We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the realtime evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photo induced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state densitymatrix renormalization group method for electron-phonon systems using local basis optimization.In our examples, we account for up to M ph = 40 bare phonons per site by working with O(10) optimal phonon modes.

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“…One possibility is to define suitable wave functions that can be treated within the VMC technique. In this spirit, Ohgoe and Imada have recently extended the "many-variable" VMC method to include phonon degrees of freedom [40,44], showing evidence in favor of a metallic (with weak superconducting correlations) phase between the CDW and Mott insulators at half filling. In addition, they highlighted the presence of phase separation when doping the CDW insulator.…”

Section: Introductionmentioning

confidence: 99%

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

et al. 2017

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By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional HubbardHolstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping t, the on-site electron-electron interaction U , the phonon energy ω0, and the electron-phonon coupling g. At half filling, the ground state is an antiferromagnetic insulator for U 2g 2 /ω0, while it is a charge-density-wave (or bi-polaronic) insulator for U 2g 2 /ω0. In addition to these phases, we find a superconducting phase that intrudes between them. For ω0/t = 1, superconductivity emerges when both U/t and 2g 2 /tω0 are small; then, by increasing the value of the phonon energy ω0, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.

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Variational Monte Carlo method for electron-phonon coupled systems

Cited by 27 publications

References 66 publications

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems

Charge-density-wave melting in the one-dimensional Holstein model

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

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