Dynamical bulk-boundary correspondence and dynamical quantum phase transitions in higher-order topological insulators
Tomasz Masłowski, Nicholas Sedlmayr
Abstract
Dynamical quantum phase transitions occur in dynamically evolving quantum systems when nonanalyticities occur at critical times in the return rate, a dynamical analog of the free energy. This extension of the concept of phase transitions can be brought into contact with another, namely, that of topological phase transitions in which the phase transition is marked by a change in a topological invariant. Following a quantum quench dynamical quantum phase transitions can happen in topological matter, a fact which has already been explored in one-dimensional topological insulators and in two-dimensional Chern insulators. Additionally, in one-dimensional systems a dynamical bulk boundary correspondence has been seen, related to the periodic appearance of zero modes of the Loschmidt echo itself. Here we extend both of these concepts to two-dimensional higher-order topological matter in which the topologically protected boundary modes are corner modes. We consider a minimal model which encompasses all possible forms of higher-order topology in two-dimensional topological band structures. We find that dynamical quantum phase transitions can still occur, and can occur for quenches which cross both bulk and boundary gap closings. Furthermore, a dynamical bulk boundary correspondence is also found, which takes a different form to that in one dimension.