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Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [3];  [4];  [5]
  1. Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany); OSTI
  2. Univ. of Maryland, College Park, MD (United States); Forschungszentrum Jülich (Germany)
  3. Forschungszentrum Jülich (Germany)
  4. Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany); Forschungszentrum Jülich (Germany)
  5. Rheinische Friedrich-Wilhelms-Univ. Bonn (Germany)
+ Show Author Affiliations
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.
Research Organization:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
FG02-93ER40762
OSTI ID:
1850039
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 102; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (2)

The Hubbard model with fermionic tensor networks
  • Schneider, Manuel; Ostmeyer, Johann; Jansen, Karl
  • Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0377
conference May 2022
Complex Paths Around The Sign Problem preprint January 2020

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Antiferromagnetism
Critical exponents
Electrical conductivity
Materials Science
Metal-insulator transition
Order parameters
Physics
Quantum phase transitions
Second order phase transitions