Generic theory of characterizing topological phases under quantum slow dynamics

TL;DR

This paper introduces a non-adiabatic method to characterize topological phases under slow quench dynamics using an exactly solvable model and two measurement schemes based on spin inversion surfaces, simplifying topological invariant detection.

Contribution

It proposes two novel schemes for non-adiabatic topological phase characterization using spin inversion surfaces, extending the measurement strategies beyond traditional methods.

Findings

Exact solvable multi-state Landau-Zener model for slow quench dynamics.

Two schemes for topological invariant measurement based on spin inversion surfaces.

Simplified measurement strategy using high-order surfaces and dimension reduction.

Abstract

Dynamical characterization of equilibrium topological phases has attracted considerable attention in recent years. In this paper, we make a thorough exploration of the non-adiabatic characterization of topological phases under slow quench protocol. We first propose an exactly solvable multi-state Landau-Zener model that can be directly applied to the non-adiabatic slow quench dynamics of topological systems. Then we present two different schemes to characterize the bulk topology of the system based on the so called spin inversion surface. The first one needs least number of quenching processes, but requires to measure the gradients of time-averaged spin-polarization on the SIS. The second one only needs to measure the value of time-averaged spin-polarization on the SIS, thus makes it possible to directly characterize the topological phases by introducing an extra quenching process. Moreover, high-order SIS or band inversion surface (BIS) relying on the dimension reduction approach, is also generalized to the above two different characterization schemes. One can extract the topological invariant from pairs of points with opposite signs both on the 0D highest order BIS and on the 0D highest order SIS, which greatly simplifies the measurement strategy and characterization process. In a word, superior to the sudden quench protocol, we demonstrate that the topological invariant can be captured not only by the topological information on BIS, but also on the SIS. In particular, direct characterization of topological phases based on BIS and SIS can be realized.