Stability of dynamical quantum phase transitions in disordered systems

Dynamical quantum phase transitions (DQPTs) appear at critical times (so-called Fisher zeros) of the Loschmidt amplitude G(t) =〈ψ|e^{-i H t}|ψ〉, where |ψ〉denotes the initial quantum state and H the Hamiltonian governing the nonequilibrium time evolution. So far DQPTs have mostly been investigated for systems with momentum conservation, but the fate of DQPTs in the presence of spatially uncorrelated disorder remains a largely open question. In this work we address this question by resorting to a supercell representation, which allows us to maintain a generalized version of the momentum space framework. Specifically, Fisher zeros appear as vortices of the complex phase of G(t) in the momentum-time plane; these vortices can only continuously change with the onset of disorder. Thus we hope to shed light on the dynamical behavior of disordered systems out of equilibrium.