Charge Order in the Holstein Model on a Honeycomb Lattice
Abstract
The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin-liquid phase between the semimetal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo simulations to study the Holstein model on a honeycomb lattice and explore the role of electron- phonon interactions on Dirac fermions. We show that they give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength. Furthermore, we evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.
- Authors:
-
- Univ. of California, Davis, CA (United States)
- Univ. Federal do Rio de Janeiro (Brazil)
- 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)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1612259
- Alternate Identifier(s):
- OSTI ID: 1546163
- Grant/Contract Number:
- SC0014671
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 7; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Charge density waves; Quantum phase transitions; Honeycomb lattice; Quantum Monte Carlo
Citation Formats
Zhang, Y. -X., Chiu, W. -T., Costa, N. C., Batrouni, G. G., and Scalettar, R. T. Charge Order in the Holstein Model on a Honeycomb Lattice. United States: N. p., 2019.
Web. doi:10.1103/physrevlett.122.077602.
Zhang, Y. -X., Chiu, W. -T., Costa, N. C., Batrouni, G. G., & Scalettar, R. T. Charge Order in the Holstein Model on a Honeycomb Lattice. United States. https://doi.org/10.1103/physrevlett.122.077602
Zhang, Y. -X., Chiu, W. -T., Costa, N. C., Batrouni, G. G., and Scalettar, R. T. Tue .
"Charge Order in the Holstein Model on a Honeycomb Lattice". United States. https://doi.org/10.1103/physrevlett.122.077602. https://www.osti.gov/servlets/purl/1612259.
@article{osti_1612259,
title = {Charge Order in the Holstein Model on a Honeycomb Lattice},
author = {Zhang, Y. -X. and Chiu, W. -T. and Costa, N. C. and Batrouni, G. G. and Scalettar, R. T.},
abstractNote = {The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin-liquid phase between the semimetal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo simulations to study the Holstein model on a honeycomb lattice and explore the role of electron- phonon interactions on Dirac fermions. We show that they give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength. Furthermore, we evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.},
doi = {10.1103/physrevlett.122.077602},
journal = {Physical Review Letters},
number = 7,
volume = 122,
place = {United States},
year = {Tue Feb 19 00:00:00 EST 2019},
month = {Tue Feb 19 00:00:00 EST 2019}
}
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Works referenced in this record:
Nature of the Spin Liquid State of the Hubbard Model on a Honeycomb Lattice
journal, August 2011
- Clark, B. K.; Abanin, D. A.; Sondhi, S. L.
- Physical Review Letters, Vol. 107, Issue 8
Holstein polaron
journal, July 1999
- Bonča, J.; Trugman, S. A.; Batistić, I.
- Physical Review B, Vol. 60, Issue 3
Resonating valence bonds and mean-field -wave superconductivity in graphite
journal, April 2007
- Black-Schaffer, Annica M.; Doniach, Sebastian
- Physical Review B, Vol. 75, Issue 13
Visualizing the charge density wave transition in - in real space
journal, June 2014
- Arguello, C. J.; Chockalingam, S. P.; Rosenthal, E. P.
- Physical Review B, Vol. 89, Issue 23
Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
journal, December 1998
- Kornilovitch, P. E.
- Physical Review Letters, Vol. 81, Issue 24
Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice
journal, October 2013
- Gu, Zheng-Cheng; Jiang, Hong-Chen; Sheng, D. N.
- Physical Review B, Vol. 88, Issue 15
Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near doping
journal, January 2012
- Wang, Wan-Sheng; Xiang, Yuan-Yuan; Wang, Qiang-Hua
- Physical Review B, Vol. 85, Issue 3
Numerical study of the two-dimensional Hubbard model
journal, July 1989
- White, S. R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review B, Vol. 40, Issue 1
The dynamics of charge-density waves
journal, October 1988
- Grüner, G.
- Reviews of Modern Physics, Vol. 60, Issue 4
Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons
journal, March 2016
- Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro
- Physical Review X, Vol. 6, Issue 1
Classification of charge density waves based on their nature
journal, February 2015
- Zhu, Xuetao; Cao, Yanwei; Zhang, Jiandi
- Proceedings of the National Academy of Sciences, Vol. 112, Issue 8
Quantum spin liquid emerging in two-dimensional correlated Dirac fermions
journal, April 2010
- Meng, Z. Y.; Lang, T. C.; Wessel, S.
- Nature, Vol. 464, Issue 7290
Effects of dimensionality and anisotropy on the Holstein polaron
journal, November 1999
- Romero, Aldo H.; Brown, David W.; Lindenberg, Katja
- Physical Review B, Vol. 60, Issue 20
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
journal, February 2019
- Chen, Chuang; Xu, Xiao Yan; Meng, Zi Yang
- Physical Review Letters, Vol. 122, Issue 7
Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice
journal, August 2013
- Assaad, Fakher F.; Herbut, Igor F.
- Physical Review X, Vol. 3, Issue 3
Density-matrix renormalization-group study of the polaron problem in the Holstein model
journal, March 1998
- Jeckelmann, Eric; White, Steven R.
- Physical Review B, Vol. 57, Issue 11
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
Two-dimensional Hubbard-Holstein bipolaron
journal, June 2004
- Macridin, A.; Sawatzky, G. A.; Jarrell, Mark
- Physical Review B, Vol. 69, Issue 24
Dimensionality effects on the Holstein polaron
journal, April 2002
- Ku, Li-Chung; Trugman, S. A.; Bonča, J.
- Physical Review B, Vol. 65, Issue 17
Phonon Dispersion and the Competition between Pairing and Charge Order
journal, May 2018
- Costa, N. C.; Blommel, T.; Chiu, W. -T.
- Physical Review Letters, Vol. 120, Issue 18
Dirac-point engineering and topological phase transitions in honeycomb optical lattices
journal, October 2008
- Wunsch, B.; Guinea, F.; Sols, F.
- New Journal of Physics, Vol. 10, Issue 10
Green’s function of the Holstein polaron
journal, December 2006
- Goodvin, Glen L.; Berciu, Mona; Sawatzky, George A.
- Physical Review B, Vol. 74, Issue 24
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
journal, December 2012
- Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji
- Scientific Reports, Vol. 2, Issue 1
Competing pairing channels in the doped honeycomb lattice Hubbard model
journal, September 2016
- Xu, Xiao Yan; Wessel, Stefan; Meng, Zi Yang
- Physical Review B, Vol. 94, Issue 11
Strength of Effective Coulomb Interactions in Graphene and Graphite
journal, June 2011
- Wehling, T. O.; Şaşıoğlu, E.; Friedrich, C.
- Physical Review Letters, Vol. 106, Issue 23
Principal component analysis for fermionic critical points
journal, November 2017
- Costa, Natanael C.; Hu, Wenjian; Bai, Z. J.
- Physical Review B, Vol. 96, Issue 19
Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
journal, August 2018
- Weber, Manuel; Hohenadler, Martin
- Physical Review B, Vol. 98, Issue 8
Chiral Spin-Density Wave, Spin-Charge-Chern Liquid, and Superconductivity in -Doped Correlated Electronic Systems on the Honeycomb Lattice
journal, September 2014
- Jiang, Shenghan; Mesaros, Andrej; Ran, Ying
- Physical Review X, Vol. 4, Issue 3
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
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
Quantum phonons and the charge-density-wave transition temperature: A dynamical mean-field study
journal, March 2001
- Blawid, Stefan; Millis, Andrew J.
- Physical Review B, Vol. 63, Issue 11
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
Phonons of graphene and graphitic materials derived from the empirical potential LCBOPII
journal, September 2011
- Karssemeijer, L. J.; Fasolino, Annalisa
- Surface Science, Vol. 605, Issue 17-18
Chiral superconductivity from repulsive interactions in doped graphene
journal, January 2012
- Nandkishore, Rahul; Levitov, L. S.; Chubukov, A. V.
- Nature Physics, Vol. 8, Issue 2
Density Waves and Cooper Pairing on the Honeycomb Lattice
journal, April 2008
- Honerkamp, Carsten
- Physical Review Letters, Vol. 100, Issue 14
Interactions and Phase Transitions on Graphene’s Honeycomb Lattice
journal, October 2006
- Herbut, Igor F.
- Physical Review Letters, Vol. 97, Issue 14
Holstein model in infinite dimensions
journal, September 1993
- Freericks, J. K.; Jarrell, M.; Scalapino, D. J.
- Physical Review B, Vol. 48, Issue 9
Competing many-body instabilities and unconventional superconductivity in graphene
journal, July 2012
- Kiesel, Maximilian L.; Platt, Christian; Hanke, Werner
- Physical Review B, Vol. 86, Issue 2
Charge-density-wave and superconducting states in the Holstein model on a square lattice
journal, February 1997
- Zheng, H.; Zhu, S. Y.
- Physical Review B, Vol. 55, Issue 6
Finite size scaling analysis of ising model block distribution functions
journal, June 1981
- Binder, K.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 43, Issue 2
A statistical approach to quantum mechanics
journal, April 1981
- Creutz, M.; Freedman, B.
- Annals of Physics, Vol. 132, Issue 2
Pairing in graphene: A quantum Monte Carlo study
journal, September 2011
- Ma, Tianxing; Huang, Zhongbing; Hu, Feiming
- Physical Review B, Vol. 84, Issue 12
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
Density waves in strongly correlated quantum chains
journal, September 2018
- Hohenadler, Martin; Fehske, Holger
- The European Physical Journal B, Vol. 91, Issue 9
Possible high-temperature superconducting state with a pairing symmetry in doped graphene
journal, February 2010
- Pathak, Sandeep; Shenoy, Vijay B.; Baskaran, G.
- Physical Review B, Vol. 81, Issue 8
Charge-density waves versus superconductivity in the Holstein model with next-nearest-neighbor hopping
journal, July 1992
- Vekić, M.; Noack, R. M.; White, S. R.
- Physical Review B, Vol. 46, Issue 1
The rise of graphene
journal, March 2007
- Geim, A. K.; Novoselov, K. S.
- Nature Materials, Vol. 6, Issue 3, p. 183-191
Ground-state and finite-temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
journal, August 2005
- Paiva, Thereza; Scalettar, R. T.; Zheng, W.
- Physical Review B, Vol. 72, Issue 8
Chiral d -wave superconductivity in doped graphene
journal, September 2014
- Black-Schaffer, Annica M.; Honerkamp, Carsten
- Journal of Physics: Condensed Matter, Vol. 26, Issue 42
Voltage-dependent STM image of a charge density wave
journal, May 1998
- Sacks, William; Roditchev, Dmitri; Klein, Jean
- Physical Review B, Vol. 57, Issue 20
Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems
journal, April 2014
- Dai, Jixia; Calleja, Eduardo; Alldredge, Jacob
- Physical Review B, Vol. 89, Issue 16
The rise of graphene
book, August 2009
- Rodgers, Peter; Geim, A. K.; Novoselov, K. S.
- Nanoscience and Technology: A Collection of Reviews from Nature Journals, p. 11-19
Density waves and Cooper pairing on the honeycomb lattice
text, January 2007
- Honerkamp, Carsten
- arXiv
Dirac-point engineering and topological phase transitions in honeycomb optical lattices
text, January 2008
- Wunsch, B.; Guinea, F.; Sols, F.
- arXiv
Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
text, January 2010
- Meng, Z. Y.; Lang, T. C.; Wessel, S.
- arXiv
Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice
text, January 2011
- Gu, Zheng-Cheng; Jiang, Hong-Chen; Sheng, D. N.
- arXiv
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
text, January 2012
- Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji
- arXiv
Chiral d-wave superconductivity in doped graphene
text, January 2014
- Black-Schaffer, Annica M.; Honerkamp, Carsten
- arXiv
Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
text, January 2015
- Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro
- arXiv
Density waves in strongly correlated quantum chains
text, January 2017
- Hohenadler, Martin; Fehske, Holger
- arXiv
Quantum Monte Carlo and variational approaches to the Holstein model
text, January 2003
- Hohenadler, Martin; Evertz, Hans Gerd; von der Linden, Wolfgang
- arXiv
Two-dimensional Hubbard-Holstein bipolaron
text, January 2004
- Macridin, Alexandru; Sawatzky, George. A.; Jarrell, Mark
- arXiv
Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
text, January 2004
- Paiva, Thereza; Scalettar, R. T.; Zheng, W.
- arXiv
Works referencing / citing this record:
Revealing fermionic quantum criticality from new Monte Carlo techniques
journal, August 2019
- Xu, Xiao Yan; Hong Liu, Zi; Pan, Gaopei
- Journal of Physics: Condensed Matter, Vol. 31, Issue 46
Fermi surface gapping in the Dirac material
journal, July 2019
- Corasaniti, M.; Yang, R.; Pal, A.
- Physical Review B, Vol. 100, Issue 4
Avoiding ergodicity problems in lattice discretizations of the Hubbard model
journal, August 2019
- Wynen, Jan-Lukas; Berkowitz, Evan; Körber, Christopher
- Physical Review B, Vol. 100, Issue 7
Electronic and phononic properties of a two-dimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering
journal, December 2019
- Li, Zi-Xiang; Devereaux, T. P.; Lee, Dung-Hai
- Physical Review B, Vol. 100, Issue 24
Enhancement of superconductivity by frustrating the charge order
journal, December 2019
- Li, Zi-Xiang; Cohen, Marvin L.; Lee, Dung-Hai
- Physical Review B, Vol. 100, Issue 24
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
journal, February 2019
- Chen, Chuang; Xu, Xiao Yan; Meng, Zi Yang
- Physical Review Letters, Vol. 122, Issue 7
Electron-Phonon Interactions in Flat Band Systems
text, January 2020
- Feng, Chunhan; Scalettar, Richard T.
- arXiv