The Berry phase: a topological test for the spectrum structure of frustrated quantum spin systems

TL;DR

This paper uses a topological Berry phase test to analyze the low energy spectrum of frustrated quantum spin systems, helping determine the presence of energy gaps and spectral structure differences.

Contribution

It applies a Berry phase-based topological test to investigate the spectrum structure of frustrated quantum spin systems in various dimensions and compares results with prior studies.

Findings

Identifies spectral differences between even and odd-legged systems.

Provides evidence for the existence or absence of energy gaps.

Confronts results with previous research to validate the approach.

Abstract

The nature of the low energy spectrum of frustrated quantum spin systems is investigated by means of a topological test introduced by Y. Hatsugai which enables to infer the possible existence or absence of a gap between the ground state and excited states of these systems. The test relies on the determination of an order parameter which is a Berry phase. The structure of the spectra of even and odd-legged systems in 2d and 3d is analyzed. Results are confronted with previous work.