DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 Tcdw of the half-filled two-dimensional Holstein model in square and honeycomb lattices have become available for the first time. Here, 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 Tcdw 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.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4];  [1];  [5]
  1. Univ. of California, Davis, CA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Chinese Academy of Sciences (CAS), Beijing (China); Univ. of Hong Kong (China); Songshan Lake Materials Lab., Guangdong (China)
  4. Chinese Academy of Sciences (CAS), Beijing (China)
  5. Univ. Côte d'Azur, Nice (France); National Univ. of Singapore (Singapore); Beijing Computational Science Research Center (China)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1844141
Report Number(s):
LA-UR-20-24119
Journal ID: ISSN 2469-9950; TRN: US2302345
Grant/Contract Number:  
89233218CNA000001; SC0014671
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 102; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Material science; Charge density waves; Electron-phonon coupling; Holstein model; Langevin algorithm; Quantum Monte Carlo

Citation Formats

Cohen-Stead, B., Barros, Kipton, Meng, ZY, Chen, Chuang, Scalettar, R. T., and Batrouni, G. G. Langevin simulations of the half-filled cubic Holstein model. United States: N. p., 2020. Web. doi:10.1103/physrevb.102.161108.
Cohen-Stead, B., Barros, Kipton, Meng, ZY, Chen, Chuang, Scalettar, R. T., & Batrouni, G. G. Langevin simulations of the half-filled cubic Holstein model. United States. https://doi.org/10.1103/physrevb.102.161108
Cohen-Stead, B., Barros, Kipton, Meng, ZY, Chen, Chuang, Scalettar, R. T., and Batrouni, G. G. Tue . "Langevin simulations of the half-filled cubic Holstein model". United States. https://doi.org/10.1103/physrevb.102.161108. https://www.osti.gov/servlets/purl/1844141.
@article{osti_1844141,
title = {Langevin simulations of the half-filled cubic Holstein model},
author = {Cohen-Stead, B. and Barros, Kipton and Meng, ZY and Chen, Chuang and Scalettar, R. T. and Batrouni, G. G.},
abstractNote = {Over the past several years, reliable quantum Monte Carlo results for the charge density wave transition temperature Tcdw of the half-filled two-dimensional Holstein model in square and honeycomb lattices have become available for the first time. Here, 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 Tcdw 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.},
doi = {10.1103/physrevb.102.161108},
journal = {Physical Review. B},
number = 16,
volume = 102,
place = {United States},
year = {Tue Oct 13 00:00:00 EDT 2020},
month = {Tue Oct 13 00:00:00 EDT 2020}
}

Works referenced in this record:

Effect of dispersive optical phonons on the behavior of a Holstein polaron
journal, August 2013


Effect of strain on charge density wave order in the Holstein model
journal, July 2019


Quantum Monte Carlo simulations and maximum entropy: Dynamics from imaginary-time data
journal, September 1991


Sign problem in the numerical simulation of many-electron systems
journal, May 1990


Hubbard model in infinite dimensions: A quantum Monte Carlo study
journal, July 1992


Revisiting the hybrid quantum Monte Carlo method for Hubbard and electron-phonon models
journal, February 2018


Studies of polaron motion
journal, November 1959


Quantum cluster theories
journal, October 2005


Langevin simulations of lattice field theories using Fourier acceleration
journal, June 1986

  • Davies, C.; Batrouni, G.; Katz, G.
  • Journal of Statistical Physics, Vol. 43, Issue 5-6
  • DOI: 10.1007/BF02628331

Numerical study of the two-dimensional Hubbard model
journal, July 1989


Accelerated Langevin simulations of lattice QCD and other models
journal, January 1987


Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data
journal, May 1996


Cellular-dynamical mean-field theory of the competition between antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
journal, March 2007


Charge Order in the Holstein Model on a Honeycomb Lattice
journal, February 2019


Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
journal, February 2019


Effects of dimensionality and anisotropy on the Holstein polaron
journal, November 1999


Self-learning quantum Monte Carlo method in interacting fermion systems
journal, July 2017


Geometry dependence of the sign problem in quantum Monte Carlo simulations
journal, July 2015


Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985


Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981


New algorithm for the numerical simulation of fermions
journal, December 1986


Dimensionality effects on the Holstein polaron
journal, April 2002


Phonon Dispersion and the Competition between Pairing and Charge Order
journal, May 2018


Quantum Monte Carlo study of strongly correlated electrons: Cellular dynamical mean-field theory
journal, May 2006


Quantum Monte Carlo algorithm for nonlocal corrections to the dynamical mean-field approximation
journal, October 2001


Competition of pairing and Peierls charge-density-wave correlations in a two-dimensional electron-phonon model
journal, July 1989

  • Scalettar, R. T.; Bickers, N. E.; Scalapino, D. J.
  • Physical Review B, Vol. 40, Issue 1
  • DOI: 10.1103/PhysRevB.40.197

Competition between phase separation and spin density wave or charge density wave order: Role of long-range interactions
journal, May 2019


Charge-density-wave-gap formation in the two-dimensional Holstein model at half-filling
journal, December 1993


Superconductivity and Charge-Density Wave Phase in the Holstein Model: a Weak Coupling Limit
journal, April 2007


Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
journal, August 2018


Hubbard model in infinite dimensions
journal, March 1992


Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study
journal, April 2018


Complexity in Strongly Correlated Electronic Systems
journal, July 2005


Pairing and charge-density-wave correlations in the Holstein model at half-filling
journal, August 1990


Quantum Monte Carlo and variational approaches to the Holstein model
journal, January 2004

  • Hohenadler, Martin; Evertz, Hans Gerd; von der Linden, Wolfgang
  • Physical Review B, Vol. 69, Issue 2
  • DOI: 10.1103/PhysRevB.69.024301

Solution of the sign problem for the half-filled Hubbard-Holstein model
journal, November 2018


Constrained path Monte Carlo method for fermion ground states
journal, March 1997


Charge-density-wave and pairing susceptibilities in a two-dimensional electron-phonon model
journal, February 1991


Diagrammatic Monte Carlo for correlated fermions
journal, April 2010


Symmetry-enforced self-learning Monte Carlo method applied to the Holstein model
journal, July 2018


Quantum Monte Carlo with the Langevin Equation: Coupled Bose-Fermi Systems
journal, October 2019


Correlated Lattice Fermions in d = Dimensions
journal, January 1989


Charge-density-wave and superconducting states in the Holstein model on a square lattice
journal, February 1997


A Novel Technique for the Simulation of Interacting Fermion Systems
journal, April 1989


Langevin simulations of lattice field theories
journal, November 1985


Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

  • Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
  • Reviews of Modern Physics, Vol. 68, Issue 1
  • DOI: 10.1103/RevModPhys.68.13

Langevin simulations of a long-range electron-phonon model
journal, January 2019


Charge-density waves versus superconductivity in the Holstein model with next-nearest-neighbor hopping
journal, July 1992


Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo
journal, May 2013


Experimental Predictions of Lattice and Perturbative Quantum Chromodynamics
journal, December 1985