Detecting and characterising dynamical quantum phase transitions through higher moments

One conception of a dynamical quantum phase transition (DQPT) is the appearance of non-analyticies in the return rate (Loschmidt Echo), which is the overlap of an initial

state at t=0 with a time-evolved state at time t with respect to a global quench. I will present an algorithm for calculating the moments of the return rate for translationally

invariant infinite MPS, which is expressed in terms of the spectrum of the mixed transfer matrix. This leads naturally to analogues of Fisher and Lee-Yang zeros for the return rate

and a topological interpretation/classification of DQPT's.