Aperiodic and quasi-periodic dynamical quantum phase transitions in multi-band topological insulators

Dynamical quantum phase transitions are non-equilibrium phenomena where non-analyticities occur in dynamically evolving correlation functions, in analogy with the non-analyticities in the derivatives of the free energy for a standard phase transition. Topological phase transitions sperate phases of equivalent symmetry but different topology. The ways in which these two phenomena can be connected has recently become a topic of great interest. Here we will report on dynamical phase transitons in many-band one dimensional topological insulators which demonstrate curious quaisi-periodic, rather than periodic, dynamical phase transitions. Furthermore we will consider the role of the topologically protected edge states in the dynamics and connections with fidelity susceptibility and dynamical entanglement entropy.