Anderson localization in a correlated fermionic mixture

TL;DR

This paper investigates Anderson localization in a two-species fermionic mixture on an optical lattice, revealing a temperature-driven transition from delocalized to localized states with a critical exponent near 0.88.

Contribution

It introduces a model combining thermal and quantum fluctuations in a fermionic mixture and numerically studies the localization transition using transfer-matrix methods.

Findings

Localization length exhibits one-parameter scaling.

Transition from delocalized to localized states with increasing temperature.

Critical exponent of localization length approximately 0.88.

Abstract

A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution for the heavy atoms and study the localization properties of the light fermions numerically by a transfer-matrix method. In a two-dimensional system one-parameter scaling of the localization length is found with a transition from delocalized states at low temperatures to localized states at high temperature. The critical exponent of the localization length is $\nu\approx 0.88$.