Dynamical signatures of symmetry protected topology following symmetry breaking

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