The Kibble-Zurek Mechanism in a Topological Phase Transition

TL;DR

This paper extends the Kibble-Zurek mechanism to multi-level systems and applies it to analyze the quenching dynamics of 1D topological superconductors with open boundaries, highlighting the role of Majorana zero modes.

Contribution

The paper generalizes the Kibble-Zurek mechanism to multi-level systems and demonstrates its effectiveness in describing the dynamics of 1D topological superconductors with open boundaries.

Findings

Generalized KZM predictions match numerical results

Open boundary conditions crucial for zero-mode Majorana states

Analysis of quenching dynamics in 1D topological superconductors

Abstract

The Kibble-Zurek mechanism (KZM) is generalized to a class of multi-level systems and applied to study the quenching dynamics of one-dimensional (1D) topological superconductors (TS) with open ends. Unlike the periodic boundary condition, the open boundary condition, that is crucial for the zero-mode Majorana states localized at the boundaries, requires to consider many coupled levels. which is ultimately related to the zero-mode Majorana modes. Our generalized KZM predictions agree well with the numerically exact results for the 1D TS.