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arXiv · 2411.16851

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

Roopayan Ghosh·Madhumita Sarkar·Ivan M. Khaymovich
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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 \(κ\) to the Rosenzweig-Porter (RP) model with fractal on-site disorder and surprisingly see that, as \(κ\) 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 $κ$ 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.

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Roopayan Ghosh, Madhumita Sarkar, Ivan M. Khaymovich. 2025-07-02. Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model. https://doi.org/10.1103/k957-fcmh

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