One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling
Abstract
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling g to the phonons drives the system towards a Peierls charge density wave state, whereas increasing the electron-electron interaction U drives the fermions into a Mott antiferromagnet. At low g and U, or when doped, the system is metallic. In one dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long-range coupling to phonons, with characteristic range ξ, interpolating between the Holstein and Fröhlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range ξ and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction U will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. Furthermore, the phase separation region is once again present in the U ≠ 0 case, even for small values of the coupling range.
- Authors:
-
- Univ. Côte d'Azur (France)
- Univ. of California, Davis, CA (United States)
- Loyola Univ. New Orleans, LA (United States)
- Univ. Côte d'Azur (France); CNRS-UNS-NUS-NTU International Joint Research Unit (Singapore); National Univ. of Singapore (Singapore); Beijing Computational Science Research Center (China)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1612258
- Alternate Identifier(s):
- OSTI ID: 1493648
- Grant/Contract Number:
- SC0014671
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 7; 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; Materials Science; Physics; Electron-phonon coupling; Holstein model; Hubbard model; Quantum Monte Carlo
Citation Formats
Hébert, Frederic, Xiao, Bo, Rousseau, V. G., Scalettar, R. T., and Batrouni, G. G. One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.075108.
Hébert, Frederic, Xiao, Bo, Rousseau, V. G., Scalettar, R. T., & Batrouni, G. G. One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling. United States. https://doi.org/10.1103/physrevb.99.075108
Hébert, Frederic, Xiao, Bo, Rousseau, V. G., Scalettar, R. T., and Batrouni, G. G. Wed .
"One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling". United States. https://doi.org/10.1103/physrevb.99.075108. https://www.osti.gov/servlets/purl/1612258.
@article{osti_1612258,
title = {One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling},
author = {Hébert, Frederic and Xiao, Bo and Rousseau, V. G. and Scalettar, R. T. and Batrouni, G. G.},
abstractNote = {The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling g to the phonons drives the system towards a Peierls charge density wave state, whereas increasing the electron-electron interaction U drives the fermions into a Mott antiferromagnet. At low g and U, or when doped, the system is metallic. In one dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long-range coupling to phonons, with characteristic range ξ, interpolating between the Holstein and Fröhlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range ξ and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction U will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. Furthermore, the phase separation region is once again present in the U ≠ 0 case, even for small values of the coupling range.},
doi = {10.1103/physrevb.99.075108},
journal = {Physical Review B},
number = 7,
volume = 99,
place = {United States},
year = {Wed Feb 06 00:00:00 EST 2019},
month = {Wed Feb 06 00:00:00 EST 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 6 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Electrons in lattice fields
journal, July 1954
- Fröhlich, H.
- Advances in Physics, Vol. 3, Issue 11, p. 325-361
Mobile Small Polaron
journal, January 1999
- Alexandrov, A. S.; Kornilovitch, P. E.
- Physical Review Letters, Vol. 82, Issue 4
Lattice polaron formation: Effects of nonscreened electron-phonon interaction
journal, March 2000
- Fehske, H.; Loos, J.; Wellein, G.
- Physical Review B, Vol. 61, Issue 12
Metallicity in the half-filled Holstein-Hubbard model
journal, November 2008
- Fehske, H.; Hager, G.; Jeckelmann, E.
- EPL (Europhysics Letters), Vol. 84, Issue 5
Peierls-insulator Mott-insulator transition in 1D
journal, March 2002
- Fehske, H.; Wellein, G.; Weiße, A.
- Physica B: Condensed Matter, Vol. 312-313
Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model
journal, November 2014
- Nocera, A.; Soltanieh-ha, M.; Perroni, C. A.
- Physical Review B, Vol. 90, Issue 19
Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
journal, October 2007
- Tezuka, Masaki; Arita, Ryotaro; Aoki, Hideo
- Physical Review B, Vol. 76, Issue 15
Phase Diagram of the One-Dimensional Holstein Model of Spinless Fermions
journal, June 1998
- Bursill, Robert J.; McKenzie, Ross H.; Hamer, Chris J.
- Physical Review Letters, Vol. 80, Issue 25
Pairing and charge-density-wave correlations in the Holstein model at half-filling
journal, August 1990
- Marsiglio, F.
- Physical Review B, Vol. 42, Issue 4
Phase Diagram of Bose-Fermi Mixtures in One-Dimensional Optical Lattices
journal, May 2006
- Pollet, Lode; Troyer, Matthias; Van Houcke, Kris
- Physical Review Letters, Vol. 96, Issue 19
Metal-insulator transition in the one-dimensional Holstein model at half filling
journal, September 1999
- Jeckelmann, Eric; Zhang, Chunli; White, Steven R.
- Physical Review B, Vol. 60, Issue 11
Effect of Quantum Fluctuations on the Peierls Instability: A Monte Carlo Study
journal, August 1982
- Hirsch, Jorge E.; Fradkin, Eduardo
- Physical Review Letters, Vol. 49, Issue 6
Fröhlich polaron and bipolaron: recent developments
journal, May 2009
- Devreese, Jozef T.; Alexandrov, Alexandre S.
- Reports on Progress in Physics, Vol. 72, Issue 6
Density-Matrix Renormalization Group Study of Pairing when Electron-Electron and Electron-Phonon Interactions Coexist: Effect of the Electronic Band Structure
journal, November 2005
- Tezuka, Masaki; Arita, Ryotaro; Aoki, Hideo
- Physical Review Letters, Vol. 95, Issue 22
Finite-size effects in Luther-Emery phases of Holstein and Hubbard models
journal, December 2015
- Greitemann, J.; Hesselmann, S.; Wessel, S.
- Physical Review B, Vol. 92, Issue 24
Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity
journal, June 2017
- Lavanya, Ch. Uma; Sankar, I. V.; Chatterjee, Ashok
- Scientific Reports, Vol. 7, Issue 1
Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
journal, March 2003
- Kuklov, A. B.; Svistunov, B. V.
- Physical Review Letters, Vol. 90, Issue 10
Holstein model in infinite dimensions
journal, September 1993
- Freericks, J. K.; Jarrell, M.; Scalapino, D. J.
- Physical Review B, Vol. 48, Issue 9
Quantum Monte Carlo study of the one-dimensional Holstein model of spinless fermions
journal, April 1996
- McKenzie, Ross H.; Hamer, C. J.; Murray, D. W.
- Physical Review B, Vol. 53, Issue 15
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems
journal, August 1998
- Prokof’ev, N. V.; Svistunov, B. V.; Tupitsyn, I. S.
- Journal of Experimental and Theoretical Physics, Vol. 87, Issue 2
Extended versus standard Holstein model: Results in two and three dimensions
journal, September 2014
- Chandler, Carl J.; Marsiglio, F.
- Physical Review B, Vol. 90, Issue 12
Langevin simulations of lattice field theories
journal, November 1985
- Batrouni, G. G.; Katz, G. R.; Kronfeld, A. S.
- Physical Review D, Vol. 32, Issue 10
Bound Electron Pairs in a Degenerate Fermi Gas
journal, November 1956
- Cooper, Leon N.
- Physical Review, Vol. 104, Issue 4
Superconductivity in the Half-Filled Hubbard-Holstein Model in the Antiadiabatic Region
journal, June 1996
- Takada, Yasutami
- Journal of the Physical Society of Japan, Vol. 65, Issue 6
Stochastic Green function algorithm
journal, May 2008
- Rousseau, V. G.
- Physical Review E, Vol. 77, Issue 5
Superconductivity in a Hubbard-Fröhlich model and in cuprates
journal, June 2009
- Hardy, T. M.; Hague, J. P.; Samson, J. H.
- Physical Review B, Vol. 79, Issue 21
Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
journal, September 2012
- Hohenadler, Martin; Assaad, Fakher F.; Fehske, Holger
- Physical Review Letters, Vol. 109, Issue 11
Langevin simulations of a long-range electron-phonon model
journal, January 2019
- Batrouni, G. G.; Scalettar, Richard T.
- Physical Review B, Vol. 99, Issue 3
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
Quantum Monte Carlo simulation in the canonical ensemble at finite temperature
journal, May 2006
- Van Houcke, K.; Rombouts, S. M. A.; Pollet, L.
- Physical Review E, Vol. 73, Issue 5
Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
journal, February 2013
- Hohenadler, Martin; Assaad, Fakher F.
- Physical Review B, Vol. 87, Issue 7
Vertex function for the coupling of an electron with intramolecular phonons: Exact results in the antiadiabatic limit
journal, November 1995
- Takada, Yasutami; Higuchi, Takatoshi
- Physical Review B, Vol. 52, Issue 17
Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling
journal, June 2007
- Hardikar, R. P.; Clay, R. T.
- Physical Review B, Vol. 75, Issue 24
Possibility of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the one-dimensional Hubbard-Holstein model at half filling
journal, February 2003
- Takada, Yasutami; Chatterjee, Ashok
- Physical Review B, Vol. 67, Issue 8
Directed update for the stochastic Green function algorithm
journal, November 2008
- Rousseau, V. G.
- Physical Review E, Vol. 78, Issue 5
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
�ber das Paulische �quivalenzverbot
journal, September 1928
- Jordan, P.; Wigner, E.
- Zeitschrift f�r Physik, Vol. 47, Issue 9-10
Phase diagram of one-dimensional electron-phonon systems. II. The molecular-crystal model
journal, April 1983
- Hirsch, Jorge E.; Fradkin, Eduardo
- Physical Review B, Vol. 27, Issue 7