Dynamical topological quantum phase transitions in high-order topological systems

We investigate the nonequilibrium dynamics of two multiband boundary-obstructed topological systems (BOTSs) and a higher-order topological superconductor (HOTSC). The singular behavior exhibited by the dynamical free energy indicates the presence of dynamical quantum phase transitions (DQPTs) within these systems. By studying the nonequilibrium dynamics in the BOTS featuring even-parity Cooper pairing, we find that there are DQPTs in this BOTS via quenching from different topological phase regions. The analysis of the energy spectra shows that two previously considered identical topological phases are actually different. Based on this result, we identify that all DQPTs in the BOTS featuring even-parity Cooper pairing result from topology-changing quenches. Moreover, we also study DQPTs in another BOTS featuring odd-parity Cooper pairing, and we obtain similar results to those from the BOTS featuring even-parity Cooper pairing. The appearance of DQPTs in different BOTSs reveals that the occurrence of DQPTs is related to the topology of BOTSs. In addition, we adopt the same method to investigate DQPT in HOTSC for comparison. The numerical results show that DQPT always takes place for quenches between topological and trivial phases. This is completely different from the results of BOTSs, for which not all topology-changing quenches are accompanied by DQPTs. The study of DQPTs unveils the apparent difference between BOTS and HOTSC, and thus our study provides an alternative approach to revealing the topological nature of novel higher-order topological systems, which does not rely on the specific definitions of topological invariants.