Title: Entanglement Dynamics of Disordered Quantum $XY$ Chains

Abstract: One of the expected signatures of Many-Body Localization is logarithmic (as opposed to ballistic) growth of bipartite entanglement starting from a product initial condition. For a class of disordered quantum $XY$ chains, and a large class of product initial states, we prove that the entanglement satisfies a constant bound, independent of time and system size. Therefore, although disordered $XY$ chains display many of the expected generic features of Many-Body Localization, the dynamics of entanglement appears to be even more strongly localized than is generically expected and observed numerically in other model systems. (Work in collaboration with
Houssam Abdul-Rahman (U Alabama at Birmingham), Robert Sims (U Arizona), and Gunter Stolz (U Alabama at Birmingham). This research was supported by the National Science Foundation under Grants DMS-1069320 (G.S.) and DMS-1515850 (B.N.), and by a grant from the Simons Foundation (#301127 to R.S.).)