Lattice Monte Carlo for Quantum Hall States on a Torus

Abstract

Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum to lattice. We first apply this new technique to study the Berry phase of transporting composite fermions along different closed paths enclosing or not enclosing the Fermi surface center in the half filled Landau level problem. The Monte Carlo result agrees with the phase structure we found on small systems and confirms it on much larger sizes. Several other quantities including the Coulomb energy in different Landau levels, structure factor, particle-hole symmetry are computed and discussed for various model states. In the end, based on certain knowledge of structure factor, we introduce a algorithm by which the lattice Monte Carlo efficiency is further boosted by several orders.

References in corpus (8)

• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Berry phase and model wavefunction in the half-filled Landau Level
• A modular-invariant modified Weierstrass sigma-function as a building block for lowest-Landau-level wavefunctions on the torus
• The origin of holomorphic states in Landau levels from non-commutative geometry, and a new formula for their overlaps on the torus
• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
• Trial wave functions for a Composite Fermi liquid on a torus
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing

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