Theory Colloquium Heyl: Dynamical quantum phase transitions

Dynamical quantum phase transitions

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic
description. As a consequence, constraints such as the principle of equal a
priori probabilities in the microcanonical ensemble can be relaxed, which can
lead to quantum states with novel properties of genuine nonequilibrium nature.
However, for the theoretical description it is in general not sufficient to
understand nonequilibrium dynamics on the basis of the properties of the
involved Hamiltonians. Instead it becomes important to characterize time-
evolution operators which adds time as an additional scale to the problem. In
this talk I will summarize recent progress in the field of dynamical quantum
phase transitions, which are phase transitions in time with temporal
nonanalyticities in matrix elements of the time-evolution operator. These
transitions are therefore not driven by an external control parameter, but
rather occur due to sharp internal changes generated solely by unitary real-
time dynamics. I will discuss obtained insights on general properties of
dynamical quantum phase transitions, their physical interpretation, as well as
recent experimental observations.