skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exact diagonalization solver for extended dynamical mean-field theory

Abstract

This paper presents an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase diagram of this approximation with good accuracy. Details on the numerical treatment of the large Hilbert space of the auxiliary Holstein-Anderson impurity problem are provided. Benchmarks with a numerically exact strong-coupling continuous-time quantum Monte Carlo solver show better convergence behavior of the exact diagonalization in the deep insulator. Special attention is given to possible effects due to the discretization of the bosonic bath. We discuss the quality of real axis spectra and address the question of screening in the Mott insulator within extended dynamical mean-field theory.

Authors:
 [1];  [2];  [3];  [1];  [4]
  1. Ural Federal Univ., Ekaterinburg (Russia). Theoretical Physics and Applied Mathematics Dept.
  2. Ural Federal Univ., Ekaterinburg (Russia). Theoretical Physics and Applied Mathematics Dept.; Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Physics
  3. Univ. of Hamburg (Germany). Inst. for Theoretical Physics
  4. Ural Federal Univ., Ekaterinburg (Russia). Theoretical Physics and Applied Mathematics Dept.; Univ. of Hamburg (Germany). Inst. for Theoretical Physics
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1544341
Alternate Identifier(s):
OSTI ID: 1416444
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 23; 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

Citation Formats

Medvedeva, Darya, Iskakov, Sergei, Krien, Friedrich, Mazurenko, Vladimir V., and Lichtenstein, Alexander I. Exact diagonalization solver for extended dynamical mean-field theory. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.235149.
Medvedeva, Darya, Iskakov, Sergei, Krien, Friedrich, Mazurenko, Vladimir V., & Lichtenstein, Alexander I. Exact diagonalization solver for extended dynamical mean-field theory. United States. doi:10.1103/PhysRevB.96.235149.
Medvedeva, Darya, Iskakov, Sergei, Krien, Friedrich, Mazurenko, Vladimir V., and Lichtenstein, Alexander I. Fri . "Exact diagonalization solver for extended dynamical mean-field theory". United States. doi:10.1103/PhysRevB.96.235149. https://www.osti.gov/servlets/purl/1544341.
@article{osti_1544341,
title = {Exact diagonalization solver for extended dynamical mean-field theory},
author = {Medvedeva, Darya and Iskakov, Sergei and Krien, Friedrich and Mazurenko, Vladimir V. and Lichtenstein, Alexander I.},
abstractNote = {This paper presents an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase diagram of this approximation with good accuracy. Details on the numerical treatment of the large Hilbert space of the auxiliary Holstein-Anderson impurity problem are provided. Benchmarks with a numerically exact strong-coupling continuous-time quantum Monte Carlo solver show better convergence behavior of the exact diagonalization in the deep insulator. Special attention is given to possible effects due to the discretization of the bosonic bath. We discuss the quality of real axis spectra and address the question of screening in the Mott insulator within extended dynamical mean-field theory.},
doi = {10.1103/PhysRevB.96.235149},
journal = {Physical Review B},
issn = {2469-9950},
number = 23,
volume = 96,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Discrete probability distribution of the total number of bosons. Each data point corresponds to the probability of finding the respective number of bosons excited. The data points agree very well with an exponential decay for all considered parameters.

Save / Share:

Works referenced in this record:

Dynamical screening in correlated electron systems—from lattice models to realistic materials
journal, July 2016


Numerical renormalization-group study of the symmetric Anderson-Holstein model: Phonon and electron spectral functions
journal, July 2003


Capturing nonlocal interaction effects in the Hubbard model: Optimal mappings and limits of applicability
journal, October 2016


Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined G W and dynamical mean field theory
journal, March 2013


Dual boson approach to collective excitations in correlated fermionic systems
journal, May 2012


Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
journal, December 2014

  • van Loon, Erik G. C. P.; Lichtenstein, Alexander I.; Katsnelson, Mikhail I.
  • Physical Review B, Vol. 90, Issue 23
  • DOI: 10.1103/PhysRevB.90.235135

Extended dynamical mean-field study of the Hubbard model with long-range interactions
journal, November 2014


Updated core libraries of the ALPS project
journal, April 2017


Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory
journal, June 2017


Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011

  • Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
  • Reviews of Modern Physics, Vol. 83, Issue 2
  • DOI: 10.1103/RevModPhys.83.349

Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model
journal, October 1996


Quantum criticality of the sub-Ohmic spin-boson model
journal, February 2012


Emerging Nonvolatile Memories to Go Beyond Scaling Limits of Conventional CMOS Nanodevices
journal, January 2014

  • Wang, Lei; Yang, CiHui; Wen, Jing
  • Journal of Nanomaterials, Vol. 2014
  • DOI: 10.1155/2014/927696

Microscopic conditions favoring itinerant ferromagnetism
journal, November 1998


Electronic structure calculations with dynamical mean-field theory
journal, August 2006


Self-energy-functional approach to systems of correlated electrons
journal, April 2003


Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
journal, December 2003


Optimal Hubbard Models for Materials with Nonlocal Coulomb Interactions: Graphene, Silicene, and Benzene
journal, July 2013


Effective-action approach to strongly correlated fermion systems
journal, March 2001


Continuous-Time Quantum Monte Carlo Method for the Coqblin–Schrieffer Model
journal, November 2007

  • Otsuki, Junya; Kusunose, Hiroaki; Werner, Philipp
  • Journal of the Physical Society of Japan, Vol. 76, Issue 11
  • DOI: 10.1143/JPSJ.76.114707

The Interplay of Long Range Interactions and Electron Density Distributions in Polar and Strongly Correlated Materials
journal, September 2016

  • Kristoffel, Nikolai; Pishtshev, Aleksandr; Rubin, Pavel
  • Journal of Superconductivity and Novel Magnetism, Vol. 30, Issue 1
  • DOI: 10.1007/s10948-016-3765-y

Low-Energy Models for Correlated Materials: Bandwidth Renormalization from Coulombic Screening
journal, September 2012


Extended dynamical mean-field theory and GW method
journal, August 2002


Antiferromagnetism and d -wave superconductivity in cuprates: A cluster dynamical mean-field theory
journal, October 2000


Spatial correlations in dynamical mean-field theory
journal, February 2000


Self-consistent dual boson approach to single-particle and collective excitations in correlated systems
journal, January 2016


Monte Carlo Method for Magnetic Impurities in Metals
journal, June 1986


Efficient variational approach to the impurity problem and its application to the dynamical mean-field theory
journal, July 2013


Effect of Long Range Coulomb Interactions on the Mott Transition
journal, April 2000


Role of direct exchange and Dzyaloshinskii-Moriya interactions in magnetic properties of graphene derivatives: C 2 F and C 2 H
journal, December 2016


Spin-orbit coupling and magnetic interactions in Si(111):{C,Si,Sn,Pb}
journal, December 2016


Correlated Electron Materials and Field Effect Transistors for Logic: A Review
journal, January 2013


Dynamical mean-field approach with predictive power for strongly correlated materials
journal, July 2017


Metal-insulator transitions
journal, October 1998

  • Imada, Masatoshi; Fujimori, Atsushi; Tokura, Yoshinori
  • Reviews of Modern Physics, Vol. 70, Issue 4, p. 1039-1263
  • DOI: 10.1103/RevModPhys.70.1039

Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity
journal, March 1994


Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
journal, October 2001


Exact Diagonalization Methods for Quantum Systems
journal, January 1993

  • Lin, H. Q.; Gubernatis, J. E.; Gould, Harvey
  • Computers in Physics, Vol. 7, Issue 4
  • DOI: 10.1063/1.4823192

Correlated electrons in high-temperature superconductors
journal, July 1994


Numerical renormalization group calculations for the self-energy of the impurity Anderson model
journal, September 1998


From local to nonlocal correlations: The Dual Boson perspective
journal, November 2016


The Kondo Resonance in Electron Spectroscopy
journal, January 2005

  • W. Allen, J.
  • Journal of the Physical Society of Japan, Vol. 74, Issue 1
  • DOI: 10.1143/JPSJ.74.34

Correlated Lattice Fermions in d = Dimensions
journal, January 1989


The Metal–Insulator Transition in the Hubbard Model at zero Temperature ii
journal, April 1994

  • Rozenberg, Marcelo J.; Moeller, Goetz; Kotliar, Gabriel
  • Modern Physics Letters B, Vol. 08, Issue 08n09
  • DOI: 10.1142/S0217984994000571

Mott-Anderson transition in disordered charge-transfer model: Insights from typical medium theory
journal, April 2014


Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration
journal, July 2002


Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model
journal, May 2013


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

Numerical renormalization group study of the Anderson-Holstein impurity model
journal, December 2001


Nonlocal dynamical correlations of strongly interacting electron systems
journal, September 1998


Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
journal, April 2013

  • Hafermann, Hartmut; Werner, Philipp; Gull, Emanuel
  • Computer Physics Communications, Vol. 184, Issue 4
  • DOI: 10.1016/j.cpc.2012.12.013

Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory
journal, October 2012


Variational Cluster Approach to Correlated Electron Systems in Low Dimensions
journal, November 2003


Stochastic method for analytic continuation of quantum Monte Carlo data
journal, May 1998


Charge ordering and correlation effects in the extended Hubbard model
journal, March 2017