Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system

One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in case where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium one particular symmetry-broken state is chosen due to the presence of an infinitesimal symmetry-breaking perturbation. We study the analogous scenario from a dynamical point of view: Can an infinitesimal symmetry-breaking perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.