Wavefunction and level statistics of random two dimensional gauge fields

TL;DR

This paper investigates wavefunction and level statistics in two-dimensional lattice clusters with random magnetic fluxes, revealing a transition from Wigner-Dyson to Poisson statistics with increasing system size and discussing localization properties.

Contribution

It provides new insights into the statistical behavior of wavefunctions and energy levels in 2D disordered gauge fields, including experimental implications and comparisons with time-reversal invariant systems.

Findings

Statistics transition from Wigner-Dyson to Poisson with size

Rapid scaling near band edges, slow within the band

Wavefunction statistics could distinguish localization scenarios

Abstract

Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2) Phi_0 with Phi_0 the flux quantum. All considered statistics start close to the corresponding Wigner-Dyson distribution for small system sizes and monotonically move towards Poisson statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for states well within the band. Localization properties are discussed considering two different scenarios. Experimental measurement of one of the considered statistics --wavefunction statistics seems the most promising one-- could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences with the Hermitian model.