Dynamical signatures of symmetry protected topology following symmetry breaking

TL;DR

This paper explores how symmetry protected topological (SPT) systems exhibit dynamical topological signatures after symmetry breaking, revealing robust non-equilibrium indicators of topology in both pure and ensemble states.

Contribution

It demonstrates that symmetry breaking and quench dynamics can reveal topological features in SPT systems, introducing the concept of dynamical many-body topology (DMBT).

Findings

Dynamical signatures can probe equilibrium topological phases.

Spontaneous symmetry breaking leads to quantized many-body invariants.

Signatures are robust across pure states and ensembles.

Abstract

We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break the protecting symmetry. Na\"ively, 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 the 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 non-equilibrium signatures should be quite generic in SPT systems, regardless of protecting symmetries or spatial dimension.