Winding numbers of phase transition points for one-dimensional topological systems

TL;DR

This paper introduces a method to characterize topological phase transition points in one-dimensional systems using winding numbers defined around gap closing points, overcoming previous limitations.

Contribution

It proposes a novel scheme to assign winding numbers to phase transition points, enabling better understanding of topological changes in 1D systems.

Findings

Winding numbers effectively characterize topological phase transitions.

Application to extended Kitaev and SSH models demonstrates the scheme's validity.

Winding numbers reflect changes in topological invariants across phase transitions.

Abstract

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.