Classification of Classical Spin Liquids: Typology and Resulting Landscape

TL;DR

This paper introduces a classification scheme for classical spin liquids based on their Hamiltonian's flat band structure, distinguishing algebraic and fragile topological types, and maps their landscape with new models.

Contribution

It provides a novel classification framework for CSLs based on flat band properties, unifying known instances and revealing transitions between different types.

Findings

Algebraic CSLs occur at transitions between fragile topological CSLs.

A new family of models demonstrates the landscape of CSLs.

The classification scheme aligns with previously known CSLs.

Abstract

Classical spin liquids (CSL) lack long-range magnetic order and are characterized by an extensive ground state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively. Each category is further classified: the algebraic case by the nature of the emergent Gauss's law at the gap-closing point(s), and the fragile topological case by the homotopy of the eigenvector winding around the Brillouin zone. Previously identified instances of CSLs fit snugly into our scheme, which finds a landscape where algebraic CSLs are located at transitions between \fragile topological ones. It also allows us to present a new, simple family of models illustrating that landscape, which hosts both fragile topological and algebraic CSLs, as well as transitions between them.