Emergent topology under slow non-adiabatic quantum dynamics

TL;DR

This paper introduces a non-adiabatic, slow quench protocol for characterizing topological phases in quantum systems, providing a minimal and unified method that works across different dimensions and quench regimes.

Contribution

It develops a generic slow quench scheme using a Coulomb-like Landau-Zener problem to characterize topological invariants without additional gradient calculations.

Findings

Topological invariants are directly obtained from spin textures on band inversion surfaces.

The method unifies sudden and adiabatic quench regimes within a single framework.

Applicable to higher-dimensional systems and various quench protocols.

Abstract

Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have focused on the ideal sudden quench regime. Here we provide a generic non-adiabatic protocol of slowly quenching the system Hamiltonian, and investigate the non-adiabatic dynamical characterization scheme of topological phase. The {\it slow} quench protocol is realized by introducing a Coulomb-like Landau-Zener problem, and it can describe, in a unified way, the crossover from sudden quench regime (deep non-adiabatic limit) to adiabatic regime. By analytically obtaining the final state vector after non-adiabatic evolution, we can calculate the time-averaged spin polarization and the corresponding topological spin texture. We find that the topological invariants of the post-quench Hamiltonian are characterized directly by the values of spin texture on the band inversion surfaces. Compared to the sudden quench regime, where one has to take an additional step to calculate the {\it gradients} of spin polarization, this non-adiabatic characterization provides a {\it minimal} scheme in detecting the topological invariants. Our findings are not restricted to 1D and 2D topological phases under Coulomb-like quench protocol, but are also valid for higher dimensional system or different quench protocol.