Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking

TL;DR

This paper investigates how long-range correlated hopping and time-reversal symmetry breaking influence Anderson localization in a 1D disordered system, revealing a transition from localized to delocalized states.

Contribution

It analytically demonstrates a correlation-induced algebraic localization robust to symmetry breaking and maps the resulting localization-delocalization transition.

Findings

Localization is algebraic and robust to finite symmetry-breaking.

A transition from subdiffusive to diffusive wavepacket spreading occurs with symmetry breaking.

The static phase diagram shows a clear boundary between localized and delocalized phases.

Abstract

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.