Euler topology in classical spin liquids

TL;DR

This paper integrates multi-gap topologies, like the Euler class, into the homotopy classification of classical spin liquids, revealing how band node braiding affects their topological and physical properties.

Contribution

It introduces the inclusion of multi-gap topologies such as the Euler class into existing homotopy classifications of spin liquids, highlighting new topological phase transitions.

Findings

Topological phases change via band node braiding.

Pinch points in spin structure factors are topologically altered.

The framework applies broadly beyond specific models.

Abstract

Classical spin liquids have recently been analyzed in view of the single-gap homotopy classification of their dispersive eigenvectors. We show that the recent progress in defining multi-gap topologies, notably exemplified by the Euler class, can be naturally included in these homotopy-based classification schemes and present phases that change topology by band node braiding. This process alters the topology of the pinch points in the spin structure factor and consequently their stability. Furthermore, we discuss how these notions also pertain to models discussed previously in the literature and have a broader range of application beyond our specific results. Our work thus opens up an uncharted avenue in the understanding of spin liquids.