Hatano-Nelson model with a periodic potential

TL;DR

This paper explores a generalized Hatano-Nelson model with periodic site energy modulation, analyzing how disorder and band gaps influence localization, spectral topology, and phase transitions through phase diagram mapping and finite size scaling.

Contribution

It introduces a generalized model combining periodic potential and disorder, and systematically studies the resulting localization and spectral properties.

Findings

Localization can be induced by disorder or band gaps.

The phase diagram reveals diverse topological phases.

Finite size scaling characterizes the localization transition.

Abstract

We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.