Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice
Abstract
We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of Uc/κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
- Authors:
-
[1];
[2];
[3];
[3];
[4];
[1]
- Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany)
- Univ. of Maryland, College Park, MD (United States); Forschungszentrum Jülich (Germany)
- Forschungszentrum Jülich (Germany)
- Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany); Forschungszentrum Jülich (Germany)
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1850039
- Grant/Contract Number:
- FG02-93ER40762
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 24; 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; Antiferromagnetism; Critical exponents; Electrical conductivity; Metal-insulator transition; Order parameters; Quantum phase transitions; Second order phase transitions
Citation Formats
Ostmeyer, Johann, Berkowitz, Evan, Krieg, Stefan, Lähde, Timo A., Luu, Thomas, and Urbach, Carsten. Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.245105.
Ostmeyer, Johann, Berkowitz, Evan, Krieg, Stefan, Lähde, Timo A., Luu, Thomas, & Urbach, Carsten. Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice. United States. https://doi.org/10.1103/physrevb.102.245105
Ostmeyer, Johann, Berkowitz, Evan, Krieg, Stefan, Lähde, Timo A., Luu, Thomas, and Urbach, Carsten. Fri .
"Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice". United States. https://doi.org/10.1103/physrevb.102.245105. https://www.osti.gov/servlets/purl/1850039.
@article{osti_1850039,
title = {Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice},
author = {Ostmeyer, Johann and Berkowitz, Evan and Krieg, Stefan and Lähde, Timo A. and Luu, Thomas and Urbach, Carsten},
abstractNote = {We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of Uc/κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.},
doi = {10.1103/physrevb.102.245105},
journal = {Physical Review. B},
number = 24,
volume = 102,
place = {United States},
year = {Fri Dec 04 00:00:00 EST 2020},
month = {Fri Dec 04 00:00:00 EST 2020}
}
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Works referenced in this record:
Is Graphene in Vacuum an Insulator?
journal, January 2009
- Drut, Joaquín E.; Lähde, Timo A.
- Physical Review Letters, Vol. 102, Issue 2
Hybrid Monte Carlo
journal, September 1987
- Duane, Simon; Kennedy, A. D.; Pendleton, Brian J.
- Physics Letters B, Vol. 195, Issue 2
JURECA: Modular supercomputer at Jülich Supercomputing Centre
journal, January 2018
- Krause, Dorian; Thörnig, Philipp
- Journal of large-scale research facilities JLSRF, Vol. 4
Many-body physics with ultracold gases
journal, July 2008
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- Reviews of Modern Physics, Vol. 80, Issue 3
Competing order in the fermionic Hubbard model on the hexagonal graphene lattice
conference, March 2017
- Buividovich, Pavel; Smith, Dominik; Ulybyshev, Maksim
- Proceedings of 34th annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)
Revisiting the hybrid quantum Monte Carlo method for Hubbard and electron-phonon models
journal, February 2018
- Beyl, Stefan; Goth, Florian; Assaad, Fakher F.
- Physical Review B, Vol. 97, Issue 8
Magnetic field driven metal-insulator phase transition in planar systems
journal, July 2002
- Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A.
- Physical Review B, Vol. 66, Issue 4
Speeding up the hybrid Monte Carlo algorithm for dynamical fermions
journal, October 2001
- Hasenbusch, Martin
- Physics Letters B, Vol. 519, Issue 1-2
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
Dynamical symmetry breaking in asymptotically free field theories
journal, November 1974
- Gross, David J.; Neveu, André
- Physical Review D, Vol. 10, Issue 10
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
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
Finite-size scaling at quantum transitions
journal, March 2014
- Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore
- Physical Review B, Vol. 89, Issue 9
Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo
journal, January 2009
- Cundy, N.; Krieg, S.; Arnold, G.
- Computer Physics Communications, Vol. 180, Issue 1
Lattice Theory for Low Energy Fermions at Nonzero Chemical Potential
journal, June 2004
- Chen, Jiunn-Wei; Kaplan, David B.
- Physical Review Letters, Vol. 92, Issue 25
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
Monte Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
journal, December 2012
- Buividovich, P. V.; Polikarpov, M. I.
- Physical Review B, Vol. 86, Issue 24
Global Monte Carlo algorithms for many-fermion systems
journal, August 1988
- Creutz, Michael
- Physical Review D, Vol. 38, Issue 4
Monte Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
journal, May 2014
- Smith, Dominik; von Smekal, Lorenz
- Physical Review B, Vol. 89, Issue 19
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
Theory of interacting electrons on the honeycomb lattice
journal, February 2009
- Herbut, Igor F.; Juričić, Vladimir; Roy, Bitan
- Physical Review B, Vol. 79, Issue 8
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
Fermionic quantum criticality in honeycomb and -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
journal, April 2015
- Parisen Toldin, Francesco; Hohenadler, Martin; Assaad, Fakher F.
- Physical Review B, Vol. 91, Issue 16
The electronic properties of graphene
journal, January 2009
- Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.
- Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162
Nuclear Lattice Effective Field Theory
book, January 2019
- Lähde, Timo A.; Meißner, Ulf-G.
- Lecture Notes in Physics
Dynamical overlap fermions, results with hybrid Monte-Carlo algorithm
journal, August 2004
- Fodor, Z.; Katz, S. D.; Szabo, K. K.
- Journal of High Energy Physics, Vol. 2004, Issue 08
Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
journal, March 2019
- Krieg, Stefan; Luu, Thomas; Ostmeyer, Johann
- Computer Physics Communications, Vol. 236
Hybrid Monte Carlo simulation on the graphene hexagonal lattice
conference, July 2012
- Brower, Richard C.; Schaich, David; Rebbi, Claudio
- Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)
Fermions on bilayer graphene: Symmetry breaking for and
journal, September 2012
- Throckmorton, Robert E.; Vafek, Oskar
- Physical Review B, Vol. 86, Issue 11
Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator
journal, June 2019
- Liu, Yuhai; Wang, Zhenjiu; Sato, Toshihiro
- Nature Communications, Vol. 10, Issue 1
Quantum Monte Carlo calculations for carbon nanotubes
journal, April 2016
- Luu, Thomas; Lähde, Timo A.
- Physical Review B, Vol. 93, Issue 15
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
Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
journal, May 2014
- Janssen, Lukas; Herbut, Igor F.
- Physical Review B, Vol. 89, Issue 20
Physical Properties of Carbon Nanotubes
book, January 1998
- Saito, R.; Dresselhaus, G.; Dresselhaus, M. S.
Critical exponents of new universality classes
journal, September 1993
- Rosenstein, B.; Kovner, A.
- Physics Letters B, Vol. 314, Issue 3-4
Mott Insulating State in Ultraclean Carbon Nanotubes
journal, January 2009
- Deshpande, V. V.; Chandra, B.; Caldwell, R.
- Science, Vol. 323, Issue 5910
Momentum Distribution and Contact of the Unitary Fermi Gas
journal, May 2011
- Drut, Joaquín E.; Lähde, Timo A.; Ten, Timour
- Physical Review Letters, Vol. 106, Issue 20
Semi-Metal-Insulator Transition of the Hubbard Model in the Honeycomb Lattice
journal, August 1992
- Sorella, S.; Tosatti, E.
- Europhysics Letters (EPL), Vol. 19, Issue 8
The Two-Dimensional Hubbard Model on the Honeycomb Lattice
journal, September 2009
- Giuliani, Alessandro; Mastropietro, Vieri
- Communications in Mathematical Physics, Vol. 293, Issue 2
Interaction-Driven Metal-Insulator Transition in Strained Graphene
journal, October 2015
- Tang, Ho-Kin; Laksono, E.; Rodrigues, J. N. B.
- Physical Review Letters, Vol. 115, Issue 18
Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response
journal, June 2017
- Stauber, T.; Parida, P.; Trushin, M.
- Physical Review Letters, Vol. 118, Issue 26
Quantum critical scaling in magnetic field near the Dirac point in graphene
journal, June 2008
- Herbut, Igor F.; Roy, Bitan
- Physical Review B, Vol. 77, Issue 24
Interactions and Phase Transitions on Graphene’s Honeycomb Lattice
journal, October 2006
- Herbut, Igor F.
- Physical Review Letters, Vol. 97, Issue 14
Numerical evidence of conformal phase transition in graphene with long-range interactions
journal, May 2019
- Buividovich, Pavel; Smith, Dominik; Ulybyshev, Maksim
- Physical Review B, Vol. 99, Issue 20
The DEEP Project An alternative approach to heterogeneous cluster-computing in the many-core era: THE DEEP PROJECT
journal, July 2015
- Eicker, Norbert; Lippert, Thomas; Moschny, Thomas
- Concurrency and Computation: Practice and Experience, Vol. 28, Issue 8
Lattice effective field theory for medium-mass nuclei
journal, May 2014
- Lähde, Timo A.; Epelbaum, Evgeny; Krebs, Hermann
- Physics Letters B, Vol. 732
Spin Fermions in the Unitary Regime: A Superfluid of a New Type
journal, March 2006
- Bulgac, Aurel; Drut, Joaquín E.; Magierski, Piotr
- Physical Review Letters, Vol. 96, Issue 9
Excitonic instability in layered degenerate semimetals
journal, May 2004
- Khveshchenko, D. V.; Leal, H.
- Nuclear Physics B, Vol. 687, Issue 3
Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
journal, June 2007
- Son, D. T.
- Physical Review B, Vol. 75, Issue 23
Lattice simulations for few- and many-body systems
journal, July 2009
- Lee, Dean
- Progress in Particle and Nuclear Physics, Vol. 63, Issue 1
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
journal, October 2014
- Wang, Lei; Corboz, Philippe; Troyer, Matthias
- New Journal of Physics, Vol. 16, Issue 10
Dirac electrons in the square-lattice Hubbard model with a -wave pairing field: The chiral Heisenberg universality class revisited
journal, December 2020
- Otsuka, Yuichi; Seki, Kazuhiro; Sorella, Sandro
- Physical Review B, Vol. 102, Issue 23
Lattice simulations for light nuclei: Chiral effective field theory at leading order
journal, January 2007
- Borasoy, B.; Epelbaum, E.; Krebs, H.
- The European Physical Journal A, Vol. 31, Issue 1
Four-loop critical exponents for the Gross-Neveu-Yukawa models
journal, November 2017
- Zerf, Nikolai; Mihaila, Luminita N.; Marquard, Peter
- Physical Review D, Vol. 96, Issue 9
The rise of graphene
journal, March 2007
- Geim, A. K.; Novoselov, K. S.
- Nature Materials, Vol. 6, Issue 3, p. 183-191
Large critical exponents for the chiral Heisenberg Gross-Neveu universality class
journal, May 2018
- Gracey, J. A.
- Physical Review D, Vol. 97, Issue 10
Hybrid Monte Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
journal, December 2018
- Buividovich, Pavel; Smith, Dominik; Ulybyshev, Maksim
- Physical Review B, Vol. 98, Issue 23
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
Quantum criticality with two length scales
journal, March 2016
- Shao, H.; Guo, W.; Sandvik, A. W.
- Science, Vol. 352, Issue 6282
Quantum critical behavior in a graphenelike model
journal, October 2008
- Hands, Simon; Strouthos, Costas
- Physical Review B, Vol. 78, Issue 16
Electron-Electron Interactions in Graphene: Current Status and Perspectives
journal, July 2012
- Kotov, Valeri N.; Uchoa, Bruno; Pereira, Vitor M.
- Reviews of Modern Physics, Vol. 84, Issue 3
Quantum Critical Behaviour in a Graphene-like Model
text, January 2008
- Hands, Simon; Strouthos, Costas
- arXiv
Interaction driven metal-insulator transition in strained graphene
text, January 2015
- Tang, Ho-Kin; Laksono, E.; Rodrigues, J. N. B.
- arXiv
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- Schneider, Manuel; Ostmeyer, Johann; Jansen, Karl
- Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)
Complex Paths Around The Sign Problem
preprint, January 2020
- Alexandru, Andrei; Basar, Gokce; Bedaque, Paulo F.
- arXiv