Characterizing the delocalized-localized Anderson phase transition based on the system's response to boundary conditions

TL;DR

This paper introduces a novel method to characterize the Anderson phase transition by analyzing how the system's eigenstates respond to changes in boundary conditions, using overlap calculations to distinguish phases.

Contribution

It presents a new approach based on boundary condition response and overlaps to identify localized, delocalized, and mobility edge states in Anderson models.

Findings

Overlap close to one in localized phase

Overlap significantly smaller in delocalized phase

Single-particle overlaps locate mobility edges

Abstract

A new characterization of the Anderson phase transition, based on the response of the system to the boundary conditions is introduced. We change the boundary conditions from periodic to antiperiodic and look for its effects on the eigenstate of the system. To characterize these effects, we use the overlap of the states. In particular, we numerically calculate the overlap between the ground-state of the system with periodic and antiperiodic boundary conditions in one-dimensional models with delocalized-localized phase transitions. We observe that the overlap is close to one in the localized phase, and it gets appreciably smaller in the delocalized phase. In addition, in models with mobility edges, we calculate the overlaps between single-particle eigenstate with periodic and antiperiodic boundary conditions to characterize the entire spectrum. By this single-particle overlap, we can locate the mobility edges between delocalized and localized states.