Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model

TL;DR

This paper uncovers a counterintuitive re-entrant localization phenomenon in a fractal Rosenzweig-Porter model, where increasing kinetic terms initially induce localization before restoring ergodicity, explained through an analytical framework and numerical results.

Contribution

It introduces a new mechanism for re-entrant localization in a fractal quantum model, combining analytical insights with numerical validation.

Findings

Increasing kinetic terms can induce localization in fractal systems.

Re-entrant delocalization transitions occur as hopping amplitude varies.

Analytical model explains the interplay between local hopping and fractal disorder.

Abstract

Typically, metallic systems localized under strong disorder exhibit a transition to \imk{delocalization} %finite conduction as kinetic terms increase. In this work, we reveal the opposite effect~--~increasing kinetic terms leads to an unexpected \imk{reduction of mobility, }%suppression of conductivity, enhancing localization of the system, and even lead to re-entrant delocalization transitions. Specifically, we add a nearest-neighbor hopping with amplitude \(\kappa\) to the Rosenzweig-Porter (RP) model with fractal on-site disorder and surprisingly see that, as \(\kappa\) grows, the system initially tends to localization from the fractal phase, but then re-enters the ergodic phase. We build an analytical framework to explain this re-entrant behavior, supported by exact diagonalization results. The interplay between the spatially local $\kappa$ term, insensitive to fractal disorder, and the energy-local RP coupling, sensitive to fine-level spacing structure, drives the observed re-entrant behavior. This mechanism offers a novel pathway to re-entrant localization phenomena in many-body quantum systems.