Quantum phase transition from the topological viewpoint

TL;DR

This paper explores quantum phase transitions characterized by topological properties rather than symmetry breaking, using a $G$-cobordism framework to analyze and identify new quantum phases.

Contribution

It introduces a unified $G$-cobordism approach to study topological quantum phase transitions, offering a novel method for investigating new quantum phases.

Findings

$G$-cobordism provides a systematic framework for topological phase transitions

The approach enables identification of previously uncharacterized quantum phases

The method unifies various topological phenomena in quantum systems

Abstract

This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase transition was investigated by $G$-cobordism in unified framework. This framework provides a useful method to investigate a new quantum phase.