Langevin Simulations of the Half-Filled Cubic Holstein Model

Abstract

Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.

References in corpus (24)

• Complexity in Strongly Correlated Electronic Systems
• Quantum Cluster Theories
• A Constrained Path Monte Carlo Method for Fermion Ground States
• Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model
• A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
• Diagrammatic Monte Carlo for Correlated Fermions
• Dimensionality effects on the Holstein polaron
• Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study
• Geometry Dependence of the Sign Problem
• Quantum Monte Carlo and variational approaches to the Holstein model
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Néel temperature and thermodynamics of the half-filled 3D Hubbard model by Diagrammatic Determinant Monte Carlo
• Self-Learning Determinantal Quantum Monte Carlo Method
• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Phonon dispersion and the competition between pairing and charge order
• Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Langevin Simulations of a Long Range Electron Phonon Model
• Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory
• Effects of dimensionality and anisotropy on the Holstein polaron
• Solution of the "sign problem" for the half filled Hubbard-Holstein model
• Effect of Strain on Charge Density Wave Order in the Holstein Model
• The effect of dispersive optical phonons on the behaviour of a Holstein polaron

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