Dynamical signatures of symmetry protected topology following symmetry breaking

We investigate topological signatures in the short-time nonequilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break a protecting symmetry. Naively one might expect that topology loses meaning when a protecting symmetry is broken. Defying this intuition, we illustrate, in an interacting Su-Schrieffer-Heeger (SSH) model, how this combination of symmetry breaking and quench dynamics can give rise to both single-particle and many-body signatures of topology. From the dynamics of the symmetry broken state, we find that we are able to dynamically probe the equilibrium topological phase diagram of a symmetry respecting projection of the post-quench Hamiltonian. In the ensemble dynamics we demonstrate how spontaneous symmetry breaking (SSB) of a protecting symmetry can result in a quantized many-body topological “invariant” which is not pinned under unitary time evolution. We dub this “dynamical many-body topology” (DMBT). We show numerically that both the pure state and ensemble signatures are remarkably robust, and argue that these nonequilibrium signatures should be quite generic in SPT systems, regardless of protecting symmetries or spatial dimension.