Detecting delocalization-localization transitions from full density distributions

TL;DR

This paper introduces a measure based on density distributions to identify delocalization-localization transitions in quantum systems, successfully applying it to various models and revealing different transition behaviors.

Contribution

It presents a novel quantitative measure for Fock-space localization from density distributions and demonstrates its effectiveness in identifying critical points in localization transitions.

Findings

Accurate critical disorder strengths for Anderson and Aubry-André models.

Different scaling behavior observed for interacting fermions, indicating a Kosterlitz-Thouless transition.

Transition points vary with filling in interacting fermion systems.

Abstract

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit that localization of particles as realized in Anderson and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localization computed from the density distributions, the occupation distance, we systematically study its scaling behavior across delocalozation transitions and identify critical points from scaling collapses of numerical data. Excellent agreement with literature results is found for the critical disorder strengths of noninteracting fermions, such as the one-dimensional Aubry-Andr\'e and the three-dimensional Anderson model. We observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition. Finally, we use our measure to extract the transition point as a function of filling for interacting fermions.