Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

TL;DR

This paper explores the rotor spectra of systems with spontaneously broken symmetries, such as antiferromagnets and QCD, highlighting the role of Berry phases and monopole fields in finite-volume quantum systems.

Contribution

It demonstrates how Berry phases and monopole fields influence rotor spectra in antiferromagnets and QCD, revealing a unified topological framework.

Findings

Rotor spectra appear in finite-volume antiferromagnets and QCD.

Berry phases induce half-integer quantization of angular momentum.

Monopole fields are central to the topological effects observed.

Abstract

The order parameter of a finite system with a spontaneously broken continuous global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with a spontaneously broken $SU(2)_s$ spin symmetry and massless QCD with a broken $SU(2)_L \times SU(2)_R$ chiral symmetry have rotor spectra when considered in a finite volume. When an electron or hole is doped into an antiferromagnet or when a nucleon is propagating through the QCD vacuum, a Berry phase arises from a monopole field and the angular momentum of the rotor is quantized in half-integer units.