Dynamical quantum phase transitions, defined in terms of the many-body Loschmidt echo, generalize the notion of phase transitions and criticality to many-body systems far from equilibrium. This rapidly advancing research field is bringing together themes from statistical physics, topological matter and strongly correlated systems. However, solving the dynamics of strongly interacting quantum systems is a notoriously difficult problem, which is hindering the progress in the field. To circumvent this impasse, I introduce a novel method to determine the singular dynamics by employing so-called Loschmidt cumulants. I will demonstrate the remarkable power of the new method by solving dynamical phase transitions in interacting Kitaev chain and spin-1 Heisenberg chain.
 S. Peotta, F. Brange, A. Deger, T. Ojanen and, C. Flindt, Physical Review X 11, 041018 (2021).
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