Berry Phases, Quantum Phase Transitions and Chern Numbers

TL;DR

This paper explores how Chern numbers, topological invariants, relate to quantum phase transitions in the XY spin-chain model, revealing their potential to distinguish different quantum phases.

Contribution

It introduces a method to compute Chern numbers via coupling to a single spin and links these invariants to quantum phase transitions.

Findings

Chern numbers can label different quantum phases.

Topological invariants provide global information about the system.

Chern numbers are related to the occurrence of quantum phase transitions.

Abstract

We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.