Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems

TL;DR

This paper reveals a universal feature of topological phase transitions across diverse systems, showing that a divergence in the curvature function characterizes the transition, enabling a unified description via a renormalization-group approach.

Contribution

It introduces a universal framework for understanding topological phase transitions across different systems using a divergence in the curvature function.

Findings

Curvature function diverges at critical points in all topological transitions.

A renormalization-group-like method describes these transitions universally.

Extends critical phenomena concepts to topological phase transitions.

Abstract

Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and driving, and hence require a variety of techniques and concepts to describe their topological properties. For instance, depending on the system, topology may be accessed from single-particle Bloch wave functions, Green's functions, or many-body wave functions. We demonstrate that despite this diversity, all topological phase transitions display a universal feature: namely, a divergence of the curvature function that composes the topological invariant at the critical point. This feature can be exploited via a renormalization-group-like methodology to describe topological phase transitions. This approach serves to extend notions of correlation function, critical exponents, scaling laws and universality classes used in Landau theory to characterize topological phase transitions in a unified manner.