Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks

TL;DR

This paper investigates how two interacting discrete time quantum walks behave under disorder, revealing a new Anderson localization phase with unique localization lengths and a complex dependence on interaction parameters.

Contribution

It introduces a novel Anderson localization regime for interacting quantum walks, showing a new localization length scale and violation of single parameter scaling.

Findings

Localization length $\xi_2$ scales with $\xi_1^{1.2}$ at $\xi_1$ for $\gamma=\pi$

Wave packets spread subdiffusively and saturate at $\xi_2$

Localization regime depends nontrivially on interaction phase $\xi_2$

Abstract

We study the interplay of two interacting discrete time quantum walks in the presence of disorder. Each walk is described by a Floquet unitary map defined on a chain of two-level systems. Strong disorder induces a novel Anderson localization phase with a gapless Floquet spectrum and one unique localization length $\xi_1$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $\gamma$. A wave packet is spreading subdiffusively beyond the bounds set by $\xi_1$ and saturates at a new length scale $\xi_2 \gg \xi_1$. In particular we find $\xi_2 \sim \xi_1^{1.2}$ for $\gamma=\pi$. We observe a nontrivial dependence of $\xi_2$ on $\gamma$, with a maximum value observed for $\gamma$-values which are shifted away from the expected strongest interaction case $\gamma=\pi$. The novel Anderson localization regime violates single parameter scaling for both interacting and noninteracting walks.