Langevin Simulations of a Long Range Electron Phonon Model

Abstract

We present a Quantum Monte Carlo (QMC) study, based on the Langevin equation, of a Hamiltonian describing electrons coupled to phonon degrees of freedom. The bosonic part of the action helps control the variation of the field in imaginary time. As a consequence, the iterative conjugate gradient solution of the fermionic action, which depends on the boson coordinates, converges more rapidly than in the case of electron-electron interactions, such as the Hubbard Hamiltonian. Fourier Acceleration is shown to be a crucial ingredient in reducing the equilibration and autocorrelation times. After describing and benchmarking the method, we present results for the phase diagram focusing on the range of the electron-phonon interaction. We delineate the regions of charge density wave formation from those in which the fermion density is inhomogeneous, caused by phase separation. We show that the Langevin approach is more efficient than the Determinant QMC method for lattice sizes $N\gtrsim 8\times 8$ and that it therefore opens a potential path to problems including, for example, charge order in the 3D Holstein model.

References in corpus (11)

• Two-dimensional Hubbard-Holstein bipolaron
• Quantum Monte Carlo and variational approaches to the Holstein model
• Phonon dispersion and the competition between pairing and charge order
• Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
• Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
• Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
• Solution of the "sign problem" for the half filled Hubbard-Holstein model
• Bipolarons from long range interactions: Singlet and triplet pairs in the screened Hubbard-Froehlich model on the chain
• A complex Langevin approach to ultracold fermions

Cited by in corpus (40)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Superconductivity and charge density wave order in the 2D Holstein model
• Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
• Antiferromagnetism induced by electron-phonon-coupling
• Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Electron-Phonon Interactions in Flat Band Systems
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• Langevin Simulations of the Half-Filled Cubic Holstein Model
• A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO${}_3$
• Effect of Strain on Charge Density Wave Order in the Holstein Model
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model
• One-dimensional Hubbard-Holstein model with finite range electron-phonon coupling
• Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study
• Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model
• Quantum Monte Carlo study of an anharmonic Holstein model
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• First-principle quantum Monte-Carlo study of charge carrier mobility in organic molecular semiconductors
• Solving quantum rotor model with different Monte Carlo techniques
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• A flexible class of exact Hubbard-Stratonovich transformations
• SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions
• Charge Singlets and Orbital-Selective Charge Density Wave Transitions
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
• Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential
• Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene
• The extended Hubbard model on a honeycomb lattice
• Reducing autocorrelation time in determinant quantum Monte Carlo using Wang-Landau algorithm: application to Holstein model
• Charge correlations suppress unconventional pairing in the Holstein model
• High-Temperature Superconductivity from Finite-Range Attractive Interaction
• Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration