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Lattice Monte Carlo for quantum Hall states on a torus

Journal Article · · Physical Review B
 [1];  [2];  [3];  [2]
  1. Princeton Univ., NJ (United States); DOE/OSTI
  2. Princeton Univ., NJ (United States)
  3. California State Univ. (CalState), Los Angeles, CA (United States)
+ Show Author Affiliations
The Monte Carlo method is very useful for studying various model states proposed for the fractional quantum Hall systems. In this paper, we introduce a lattice Monte Carlo method based on an exact lattice formalism for quantum Hall problems defined on a torus. This “lattice representation” is applied to study the many body Berry phase of the composite-Fermi liquid phase in a half-filled Landau level. Here, the Monte Carlo result agrees with the exact numerical result found on small systems sizes and is consistent with the prediction from the Dirac fermion low-energy effective theory. Many other aspects of other model states, including the structure factor, Coulomb energy and particle-hole symmetry, are studied and discussed.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0002140
OSTI ID:
1610644
Alternate ID(s):
OSTI ID: 1546184
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 12 Vol. 99; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (4)

Dirac Fermion Hierarchy of Composite Fermi Liquids journal June 2019
Hall viscosity of composite fermions journal February 2020
Dirac Fermion Hierarchy of Composite Fermi Liquids text January 2018
Hall Viscosity of Composite Fermions text January 2019

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Fractional quantum Hall effect
Materials science
Monte Carlo methods
Numerical techniques
Physics