Floquet Anderson localization of two interacting discrete time quantum walks

Abstract

© 2020 American Physical Society. 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) >> xi(1). In particular we find xi(2) similar to xi(1.2)(2) for gamma = pi. We observe a nontrivial dependence of xi(2) on gamma, with a maximum value observed for y values which are shifted away from the expected strongest interaction case gamma = pi. The novel Anderson localization regime indicates violation of single parameter scaling for both interacting and noninteracting walks