One necessary criterion for the thermalization of a nonequilibrium quantummany-particle system is ergodicity. It is, however, not sufficient in casewhere the asymptotic long-time state lies in a symmetry-broken phase but theinitial state of nonequilibrium time evolution is fully symmetric with respectto this symmetry. In equilibrium one particular symmetry-broken state is chosendue to the presence of an infinitesimal symmetry-breaking perturbation. Westudy the analogous scenario from a dynamical point of view: Can aninfinitesimal symmetry-breaking perturbation be sufficient for the system toestablish a nonvanishing order during quantum real-time evolution? We studythis question analytically for a minimal model system that can be associatedwith symmetry breaking, the ferromagnetic Kondo model. We show that after aquantum quench from a completely symmetric state the system is able to breakits symmetry dynamically and discuss how these features can be observedexperimentally.
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