Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven Su-Schrieffer-Heeger chain

Abstract

Considering a BDI symmetric one-dimensional Su-Schrieffer-Heeger model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time-dependent perturbation; the effective Hamiltonian, which generates the temporal evolution of the initial (ground) state of the completely symmetric initial Hamiltonian, may have the same or different symmetries. To exemplify, we consider the following protocols, namely (i) a perfectly periodic protocol, (ii) sudden changes in the parameters of the initial Hamiltonian. We establish that the topological invariant may change in some cases when the effective Hamiltonian (or the Floquet Hamiltonian in the periodic situation when observed stroboscopically) does not respect all BDI symmetries; this is manifested in the associated particle (polarization) or heat current in the bulk. Our results establish a strong connection between the time evolution of the winding number (thus, the associated transport of currents) and the symmetry of the Hamiltonian generating the time evolution, which has been illustrated considering an exhaustive set of possibilities. We also briefly dwell on the situation where the driving is not perfectly periodic.