Quantum selection for spin systems

TL;DR

This paper investigates the mathematical mechanisms behind quantum order by disorder in spin systems, highlighting the influence of competing factors and distinguishing it from thermal selection, with general results and illustrative models.

Contribution

It provides new mathematical insights into quantum selection processes in spin systems, including the derivation of selection rules and analysis of their behavior in toy models.

Findings

Quantum selection is governed by multiple competing contributions.

Quantum and thermal selection are not directly linked.

Quantum selection exhibits interesting behaviors in specific models.

Abstract

We report mathematical results on the process by which quantum order by disorder takes place for spin systems. The selection rules follow the influence of several competing contributions. Moreover there is no link between quantum selection and thermal selection. We present work in the general setting as well as toy models and examples for which quantum selection has an interesting behaviour.