Universal scaling of quantum state transport in one-dimensional topological chain under nonadiabatic dynamics

TL;DR

This paper investigates how quantum states are transported in a one-dimensional topological chain under nonadiabatic driving, revealing power-law scaling behaviors that differ for edge and bulk states, thus advancing understanding of quantum dynamics.

Contribution

The study extends the Kibble-Zurek mechanism to quantum state transport in topological systems, highlighting distinct scaling laws for edge and bulk states during nonadiabatic transitions.

Findings

Quantum state transport exhibits power-law scaling with driving velocity.

Edge and bulk states have different scaling exponents.

Results provide new insights into nonadiabatic quantum dynamics.

Abstract

When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by Kibble-Zurek mechanism. In this study, we generalized this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependencies of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a novel perspective on quantum state transfer and enriches the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.