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Title: Langevin simulations of a long-range electron-phonon model

Journal Article · · Physical Review. B
 [1];  [2]
  1. Univ. Côte d'Azur, Nice (France); CNRS-UCA-SU-NUS-NTU International Joint Research Unit (Singapore); National Univ. of Singapore (Singapore); Beijing Computational Science Research Center (China); DOE/OSTI
  2. Univ. of California, Davis, CA (United States)
+ Show Author Affiliations

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. Furthermore, 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 ≳ 8 × 8 and that it therefore opens a potential path to problems including, for example, charge order in the three-dimensional Holstein model.

Research Organization:
Univ. of California, Davis, CA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0014671
OSTI ID:
1612257
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 99; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (6)

The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code text January 2020
Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics text January 2021
Revealing fermionic quantum criticality from new Monte Carlo techniques journal August 2019
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons journal February 2019
Charge Order in the Holstein Model on a Honeycomb Lattice journal February 2019
Charge Order in the Holstein Model on a Honeycomb Lattice text January 2018

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