$\mathbb{Z}_{2}$ Skin Channels and Effective Dynamical Quantum Phase Transitions

TL;DR

This paper analytically investigates the $$ skin channels in non-Hermitian systems with anomalous time-reversal symmetry, revealing their role in quantum revivals and scale-dependent dynamical quantum phase transitions.

Contribution

It introduces a rigorous analysis of $$ skin channels and their connection to dynamical quantum phase transitions, expanding understanding of skin effects in non-Hermitian systems.

Findings

Skin channels exhibit exponential time evolution in momentum space.

Center of mass circulations lead to quantum revivals.

Dynamical quantum phase transitions show scale-dependent behavior.

Abstract

We analytically describe the dynamically separated $\mathbb{Z}_{2}$ skin channels (wavepacket evolutions) under periodic boundary condition (PBC) in non-Hermitian systems with anomalous time-reversal symmetry (ATRS), by combining the semiclassical worldline perspective with an enhanced understanding of skin effects. These channels, tied to the initial state and relevant symmetries, exhibit individually exponential-dominated time evolution in momentum space, where their amplitude maxima evolve toward the dominant momenta. In real space, their center of masses (COMs) circulate around the one-dimensional (1D) chain, tracing semiclassical worldlines. Such circulations imply quantum revivals and effective dynamical quantum phase transitions (DQPTs) regardless of any wavepackets' phase interference, with the latter showing scale-dependent behavior, a feature distinct from conventional DQPTs. This work rigorously demonstrates our previous findings on worldline windings and the winding-control mechanism, confirming that the core physics is shared with the ordinary skin effect.