Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench

TL;DR

This paper explores emergent topological phenomena such as dynamic Chern numbers and quantum phase transitions in non-Hermitian PT-symmetric quantum quenches, linking fixed points in the Brillouin zone to these phenomena.

Contribution

It develops a formalism within biorthogonal quantum mechanics to characterize topological properties in non-unitary dynamics and proves fixed points' existence in PT-symmetric quenches.

Findings

Fixed points occur at non-evolving states in the Brillouin zone.

Dynamic topological phenomena are linked to fixed points in PT-symmetric quenches.

Topological phenomena are absent in PT-broken regimes.

Abstract

We identify emergent topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time ($\mathcal{PT}$) symmetry. Their occurrence in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the states do not evolve in time. We construct a theoretical formalism for characterizing topological properties in non-unitary dynamics within the framework of biorthogonal quantum mechanics, and prove the existence of fixed points for quenches between distinct static topological phases in the $\mathcal{PT}$-symmetry-preserving regime. We then reveal the interesting relation between different dynamic topological phenomena through the momentum-time spin texture characterizing the dynamic process. For quenches involving Hamiltonians in the $\mathcal{PT}$-symmetry-broken regime, these topological phenomena are not ensured.