Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

TL;DR

This paper introduces a solvable multiband topological insulator model to study complex dynamical quantum phase transitions, boundary effects, entanglement entropy, and fidelity susceptibility, revealing rich quasiperiodic phenomena and topological signatures.

Contribution

It presents a new multiband model extending the SSH model, uncovering richer dynamical phase transitions and boundary effects, and explores their relation to entanglement and topological invariants.

Findings

Presence of quasiperiodic and aperiodic dynamical quantum phase transitions.

Boundary return rate plateaus linked to topological properties.

Fidelity susceptibility scales with the number of bands, indicating topological phase transitions.

Abstract

We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions can still occur for quenches within a single topological phase. We also investigate the boundary contributions from the presence of the topologically protected edge states of this model. Plateaus in the boundary return rate are related to the topology of the time evolving Hamiltonian, and hence to a dynamical bulk-boundary correspondence. We go on to consider the dynamics of the entanglement entropy generated after a quench, and its potential relation to the critical times of the dynamical quantum phase transitions. Finally, we investigate the fidelity susceptibility as an indicator of the topological phase transitions, and find a simple scaling law as a function of the number of bands of our multiband model which is found to be the same for both bulk and boundary fidelity susceptibilities.