Charge Order in the Holstein Model on a Honeycomb Lattice

Zhang, Y. -X.; Chiu, W. -T.; Costa, N. C.; Batrouni, G. G.; Scalettar, R. T.

doi:10.1103/physrevlett.122.077602

Charge Order in the Holstein Model on a Honeycomb Lattice

Journal Article · Tue Feb 19 00:00:00 EST 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.122.077602· OSTI ID:1612259

Zhang, Y. -X. ^[1]; Chiu, W. -T. ^[2]; Costa, N. C. ^[3]; Batrouni, G. G. ^[4]; Scalettar, R. T. ^[2]

Univ. of California, Davis, CA (United States); DOE/OSTI
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)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0014671

OSTI ID:: 1612259

Alternate ID(s):: OSTI ID: 1546163

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 7 Vol. 122; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

Studies of Polaron Motion Holstein, T. Annals of Physics, Vol. 281, Issue 1-2 https://doi.org/10.1006/aphy.2000.6021	journal	April 2000
Finite size scaling analysis of ising model block distribution functions Binder, K. Zeitschrift f�r Physik B Condensed Matter, Vol. 43, Issue 2 https://doi.org/10.1007/BF01293604	journal	June 1981
Studies of polaron motion Holstein, T. Annals of Physics, Vol. 8, Issue 3 https://doi.org/10.1016/0003-4916(59)90002-8	journal	November 1959
Studies of polaron motion Holstein, T. Annals of Physics, Vol. 8, Issue 3 https://doi.org/10.1016/0003-4916(59)90003-x	journal	November 1959
A statistical approach to quantum mechanics Creutz, M.; Freedman, B. Annals of Physics, Vol. 132, Issue 2 https://doi.org/10.1016/0003-4916(81)90074-9	journal	April 1981
Phonons of graphene and graphitic materials derived from the empirical potential LCBOPII Karssemeijer, L. J.; Fasolino, Annalisa Surface Science, Vol. 605, Issue 17-18 https://doi.org/10.1016/j.susc.2010.10.036	journal	September 2011
Quantum spin liquid emerging in two-dimensional correlated Dirac fermions Meng, Z. Y.; Lang, T. C.; Wessel, S. Nature, Vol. 464, Issue 7290 https://doi.org/10.1038/nature08942	journal	April 2010
The rise of graphene Geim, A. K.; Novoselov, K. S. Nature Materials, Vol. 6, Issue 3, p. 183-191 https://doi.org/10.1038/nmat1849	journal	March 2007
Chiral superconductivity from repulsive interactions in doped graphene Nandkishore, Rahul; Levitov, L. S.; Chubukov, A. V. Nature Physics, Vol. 8, Issue 2 https://doi.org/10.1038/nphys2208	journal	January 2012
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji Scientific Reports, Vol. 2, Issue 1 https://doi.org/10.1038/srep00992	journal	December 2012
Classification of charge density waves based on their nature Zhu, Xuetao; Cao, Yanwei; Zhang, Jiandi Proceedings of the National Academy of Sciences, Vol. 112, Issue 8 https://doi.org/10.1073/pnas.1424791112	journal	February 2015
Chiral d -wave superconductivity in doped graphene Black-Schaffer, Annica M.; Honerkamp, Carsten Journal of Physics: Condensed Matter, Vol. 26, Issue 42 https://doi.org/10.1088/0953-8984/26/42/423201	journal	September 2014
Dirac-point engineering and topological phase transitions in honeycomb optical lattices Wunsch, B.; Guinea, F.; Sols, F. New Journal of Physics, Vol. 10, Issue 10 https://doi.org/10.1088/1367-2630/10/10/103027	journal	October 2008
Numerical study of the two-dimensional Hubbard model White, S. R.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevB.40.506	journal	July 1989
Pairing and charge-density-wave correlations in the Holstein model at half-filling Marsiglio, F. Physical Review B, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevB.42.2416	journal	August 1990
Charge-density waves versus superconductivity in the Holstein model with next-nearest-neighbor hopping Vekić, M.; Noack, R. M.; White, S. R. Physical Review B, Vol. 46, Issue 1 https://doi.org/10.1103/PhysRevB.46.271	journal	July 1992
Holstein model in infinite dimensions Freericks, J. K.; Jarrell, M.; Scalapino, D. J. Physical Review B, Vol. 48, Issue 9 https://doi.org/10.1103/PhysRevB.48.6302	journal	September 1993
Charge-density-wave and superconducting states in the Holstein model on a square lattice Zheng, H.; Zhu, S. Y. Physical Review B, Vol. 55, Issue 6 https://doi.org/10.1103/PhysRevB.55.3803	journal	February 1997
Voltage-dependent STM image of a charge density wave Sacks, William; Roditchev, Dmitri; Klein, Jean Physical Review B, Vol. 57, Issue 20 https://doi.org/10.1103/PhysRevB.57.13118	journal	May 1998
Density-matrix renormalization-group study of the polaron problem in the Holstein model Jeckelmann, Eric; White, Steven R. Physical Review B, Vol. 57, Issue 11 https://doi.org/10.1103/PhysRevB.57.6376	journal	March 1998
Effects of dimensionality and anisotropy on the Holstein polaron Romero, Aldo H.; Brown, David W.; Lindenberg, Katja Physical Review B, Vol. 60, Issue 20 https://doi.org/10.1103/PhysRevB.60.14080	journal	November 1999
Holstein polaron Bonča, J.; Trugman, S. A.; Batistić, I. Physical Review B, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRevB.60.1633	journal	July 1999
Metal-insulator transition in the one-dimensional Holstein model at half filling Jeckelmann, Eric; Zhang, Chunli; White, Steven R. Physical Review B, Vol. 60, Issue 11 https://doi.org/10.1103/PhysRevB.60.7950	journal	September 1999
Quantum phonons and the charge-density-wave transition temperature: A dynamical mean-field study Blawid, Stefan; Millis, Andrew J. Physical Review B, Vol. 63, Issue 11 https://doi.org/10.1103/PhysRevB.63.115114	journal	March 2001
Dimensionality effects on the Holstein polaron Ku, Li-Chung; Trugman, S. A.; Bonča, J. Physical Review B, Vol. 65, Issue 17 https://doi.org/10.1103/PhysRevB.65.174306	journal	April 2002
Quantum Monte Carlo and variational approaches to the Holstein model Hohenadler, Martin; Evertz, Hans Gerd; von der Linden, Wolfgang Physical Review B, Vol. 69, Issue 2 https://doi.org/10.1103/PhysRevB.69.024301	journal	January 2004
Two-dimensional Hubbard-Holstein bipolaron Macridin, A.; Sawatzky, G. A.; Jarrell, Mark Physical Review B, Vol. 69, Issue 24 https://doi.org/10.1103/PhysRevB.69.245111	journal	June 2004
Ground-state and finite-temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice Paiva, Thereza; Scalettar, R. T.; Zheng, W. Physical Review B, Vol. 72, Issue 8 https://doi.org/10.1103/PhysRevB.72.085123	journal	August 2005
Green’s function of the Holstein polaron Goodvin, Glen L.; Berciu, Mona; Sawatzky, George A. Physical Review B, Vol. 74, Issue 24 https://doi.org/10.1103/PhysRevB.74.245104	journal	December 2006
Resonating valence bonds and mean-field d -wave superconductivity in graphite Black-Schaffer, Annica M.; Doniach, Sebastian Physical Review B, Vol. 75, Issue 13 https://doi.org/10.1103/PhysRevB.75.134512	journal	April 2007
Possible high-temperature superconducting state with a d + i d pairing symmetry in doped graphene Pathak, Sandeep; Shenoy, Vijay B.; Baskaran, G. Physical Review B, Vol. 81, Issue 8 https://doi.org/10.1103/PhysRevB.81.085431	journal	February 2010
Pairing in graphene: A quantum Monte Carlo study Ma, Tianxing; Huang, Zhongbing; Hu, Feiming Physical Review B, Vol. 84, Issue 12 https://doi.org/10.1103/PhysRevB.84.121410	journal	September 2011
Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1 4 doping Wang, Wan-Sheng; Xiang, Yuan-Yuan; Wang, Qiang-Hua Physical Review B, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevB.85.035414	journal	January 2012
Competing many-body instabilities and unconventional superconductivity in graphene Kiesel, Maximilian L.; Platt, Christian; Hanke, Werner Physical Review B, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevB.86.020507	journal	July 2012
Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice Gu, Zheng-Cheng; Jiang, Hong-Chen; Sheng, D. N. Physical Review B, Vol. 88, Issue 15 https://doi.org/10.1103/PhysRevB.88.155112	journal	October 2013
Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems Dai, Jixia; Calleja, Eduardo; Alldredge, Jacob Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165140	journal	April 2014
Visualizing the charge density wave transition in 2 H - NbSe 2 in real space Arguello, C. J.; Chockalingam, S. P.; Rosenthal, E. P. Physical Review B, Vol. 89, Issue 23 https://doi.org/10.1103/PhysRevB.89.235115	journal	June 2014
Competing pairing channels in the doped honeycomb lattice Hubbard model Xu, Xiao Yan; Wessel, Stefan; Meng, Zi Yang Physical Review B, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevB.94.115105	journal	September 2016
Principal component analysis for fermionic critical points Costa, Natanael C.; Hu, Wenjian; Bai, Z. J. Physical Review B, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevB.96.195138	journal	November 2017
Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid Weber, Manuel; Hohenadler, Martin Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085405	journal	August 2018
Langevin simulations of a long-range electron-phonon model Batrouni, G. G.; Scalettar, Richard T. Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevB.99.035114	journal	January 2019
Monte Carlo calculations of coupled boson-fermion systems. I Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L. Physical Review D, Vol. 24, Issue 8 https://doi.org/10.1103/PhysRevD.24.2278	journal	October 1981
Density Waves and Cooper Pairing on the Honeycomb Lattice Honerkamp, Carsten Physical Review Letters, Vol. 100, Issue 14 https://doi.org/10.1103/PhysRevLett.100.146404	journal	April 2008
Strength of Effective Coulomb Interactions in Graphene and Graphite Wehling, T. O.; Şaşıoğlu, E.; Friedrich, C. Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236805	journal	June 2011
Nature of the Spin Liquid State of the Hubbard Model on a Honeycomb Lattice Clark, B. K.; Abanin, D. A.; Sondhi, S. L. Physical Review Letters, Vol. 107, Issue 8 https://doi.org/10.1103/PhysRevLett.107.087204	journal	August 2011
Phonon Dispersion and the Competition between Pairing and Charge Order Costa, N. C.; Blommel, T.; Chiu, W. -T. Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/PhysRevLett.120.187003	journal	May 2018
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons Chen, Chuang; Xu, Xiao Yan; Meng, Zi Yang Physical Review Letters, Vol. 122, Issue 7 https://doi.org/10.1103/PhysRevLett.122.077601	journal	February 2019
Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron Kornilovitch, P. E. Physical Review Letters, Vol. 81, Issue 24 https://doi.org/10.1103/PhysRevLett.81.5382	journal	December 1998
Interactions and Phase Transitions on Graphene’s Honeycomb Lattice Herbut, Igor F. Physical Review Letters, Vol. 97, Issue 14 https://doi.org/10.1103/PhysRevLett.97.146401	journal	October 2006
Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice Assaad, Fakher F.; Herbut, Igor F. Physical Review X, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevX.3.031010	journal	August 2013
Chiral Spin-Density Wave, Spin-Charge-Chern Liquid, and d + i d Superconductivity in 1 / 4 -Doped Correlated Electronic Systems on the Honeycomb Lattice Jiang, Shenghan; Mesaros, Andrej; Ran, Ying Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031040	journal	September 2014
Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro Physical Review X, Vol. 6, Issue 1 https://doi.org/10.1103/PhysRevX.6.011029	journal	March 2016
The dynamics of charge-density waves Grüner, G. Reviews of Modern Physics, Vol. 60, Issue 4 https://doi.org/10.1103/RevModPhys.60.1129	journal	October 1988
Density waves in strongly correlated quantum chains Hohenadler, Martin; Fehske, Holger The European Physical Journal B, Vol. 91, Issue 9 https://doi.org/10.1140/epjb/e2018-90354-7	journal	September 2018
The rise of graphene Rodgers, Peter; Geim, A. K.; Novoselov, K. S. Nanoscience and Technology: A Collection of Reviews from Nature Journals, p. 11-19 https://doi.org/10.1142/9789814287005_0002	book	August 2009
Density waves and Cooper pairing on the honeycomb lattice Honerkamp, Carsten arXiv https://doi.org/10.48550/arxiv.0711.1259	text	January 2007
Dirac-point engineering and topological phase transitions in honeycomb optical lattices Wunsch, B.; Guinea, F.; Sols, F. arXiv https://doi.org/10.48550/arxiv.0807.4245	text	January 2008
Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions Meng, Z. Y.; Lang, T. C.; Wessel, S. arXiv https://doi.org/10.48550/arxiv.1003.5809	text	January 2010
Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice Gu, Zheng-Cheng; Jiang, Hong-Chen; Sheng, D. N. arXiv https://doi.org/10.48550/arxiv.1110.1183	text	January 2011
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji arXiv https://doi.org/10.48550/arxiv.1207.1783	text	January 2012
Chiral d-wave superconductivity in doped graphene Black-Schaffer, Annica M.; Honerkamp, Carsten arXiv https://doi.org/10.48550/arxiv.1406.0101	text	January 2014
Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro arXiv https://doi.org/10.48550/arxiv.1510.08593	text	January 2015
Density waves in strongly correlated quantum chains Hohenadler, Martin; Fehske, Holger arXiv https://doi.org/10.48550/arxiv.1706.00470	text	January 2017
Quantum Monte Carlo and variational approaches to the Holstein model Hohenadler, Martin; Evertz, Hans Gerd; von der Linden, Wolfgang arXiv https://doi.org/10.48550/arxiv.cond-mat/0305387	text	January 2003
Two-dimensional Hubbard-Holstein bipolaron Macridin, Alexandru; Sawatzky, George. A.; Jarrell, Mark arXiv https://doi.org/10.48550/arxiv.cond-mat/0401305	text	January 2004
Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice Paiva, Thereza; Scalettar, R. T.; Zheng, W. arXiv https://doi.org/10.48550/arxiv.cond-mat/0406535	text	January 2004

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