Quantum Phase Transitions Go Dynamical

Just like a thermal partition function can be a nonanalytic function of temperature, the trace of the evolution operator of a quantum system can be a nonanalytic function of time, the phenomenon somtimes referred to as dynamical quantum phase transitions. These singularities which occur at certain points in time in the evolution of a quantum system are the subject of this talk. Interestingly, they can even appear in systems which do not undergo conventional thermal or quantum phase transitions. While there might be no obvious way to measure the trace of the evolution operator directly, it is possible to observe the “return probability”, the probability that a system which underwent a quantum quench and subsequently evolved for some time finds itself back in its original state. Sharing some similarity with the trace of the evolution operator, this probability can also be singular at certain times. In the context of quantum quench dynamics these singularities were already observed experimentally. Interpreting the trace of the evolution operator in terms of spectral form factors allows to further narrow down the class of quantum systems which could feature these singularities. In particular, they can be seen in integrable and many body localized systems which can have appropriate spectral form factors, although they are not limited to these types of systems. In the absence of a comprehensive theory of these singularities, their numerical study is often the only tool at our disposal to identify relevant systems where they may be present.