Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks

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 $ξ_1$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $γ$. A wave packet is spreading subdiffusively beyond the bounds set by $ξ_1$ and saturates at a new length scale $ξ_2 \gg ξ_1$. In particular we find $ξ_2 \sim ξ_1^{1.2}$ for $γ=π$. We observe a nontrivial dependence of $ξ_2$ on $γ$, with a maximum value observed for $γ$-values which are shifted away from the expected strongest interaction case $γ=π$. The novel Anderson localization regime violates single parameter scaling for both interacting and noninteracting walks.

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