Characterization of topological phase transitions via topological properties of transition points

TL;DR

This paper introduces a method to characterize topological phase transitions by assigning topological invariants to transition points, providing a new way to understand phase changes in quantum systems.

Contribution

It proposes a novel approach to analyze topological phase transitions through invariants defined on surrounding surfaces in parameter space.

Findings

Successfully applied to SSH and Haldane models

Topological invariants reflect changes across phase transitions

Provides a new characterization method for topological phase transitions

Abstract

We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of momentum and transition driving parameter. By applying our scheme to the Su-Schrieffer-Heeger model and Haldane model, we demonstrate that the topological phase transition can be well characterized by the defined topological invariant of the transition point, which reflects the change of topological invariants of topologically different phases across the phase transition point.