Floquet Anderson localization of two interacting discrete time quantum walks
Merab Malishava, I. Vakulchyk, M. V. Fistul, Sergej Flach · Physical review. B./Physical review. B · 2020
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 ${\ensuremath{\xi}}_{1}$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $\ensuremath{\gamma}$. A wave packet is spreading subdiffusively beyond the bounds set by ${\ensuremath{\xi}}_{1}$ and saturates at a new length scale ${\ensuremath{\xi}}_{2}\ensuremath{\gg}{\ensuremath{\xi}}_{1}$. In particular we find ${\ensuremath{\xi}}_{2}\ensuremath{\sim}{\ensuremath{\xi}}_{1}^{1.2}$ for $\ensuremath{\gamma}=\ensuremath{\pi}$. We observe a nontrivial dependence of ${\ensuremath{\xi}}_{2}$ on $\ensuremath{\gamma}$, with a maximum value observed for $\ensuremath{\gamma}$ values which are shifted away from the expected strongest interaction case $\ensuremath{\gamma}=\ensuremath{\pi}$. The novel Anderson localization regime indicates violation of single parameter scaling for both interacting and noninteracting walks.