Disorder-induced two-body localised state in interacting quantum walks

TL;DR

This paper demonstrates how time-dependent disorder in an interacting quantum walk causes two-body states to localize, showing distinct entanglement growth behaviors and drawing parallels with many-body localization phenomena.

Contribution

It introduces a novel disorder-induced localization mechanism in two-body quantum walks, analyzing entanglement growth and localization length without saturation effects.

Findings

Localization length computed for two-body states

Logarithmic entanglement growth in delocalized phase

Double logarithmic entanglement growth in localized phase

Abstract

We observe the onset of non-ergodicity from ballistic propagation of a two-body bound state in an interacting discrete-time quantum walk (DTQW) due to time-dependent disorder in the interaction. The effect of the disorder on the two-body state can be interpreted as Anderson-type localisation in a projected DTQW, but without saturation of entanglement entropy. We characterise the two-body localisation in terms of the rate of growth of entanglement entropy and compute the localisation length. We find indications for two distinct growth laws for the entanglement: a logarithmic law in the delocalised phase and a double logarithmic law in the localised phase. We discuss similarities with many-body localisation (MBL).