The spin-orbital Kitaev model: from kagome spin ice to classical fractons

TL;DR

This paper introduces an exactly solvable classical spin-orbital model related to the Kitaev model, revealing connections to kagome spin ice and classical fractons, with exact solutions and a continuum gauge theory.

Contribution

It presents a new classical analogue of the Kitaev model on the ruby lattice, with exact solutions and a novel connection to classical kagome spin ice and fracton physics.

Findings

Exact partition function and structure factor derived

Mapping between honeycomb and kagome spin models established

Identification of classical fractons with immobile excitations

Abstract

We study an exactly solvable spin-orbital model that can be regarded as a classical analogue of the celebrated Kitaev honeycomb model and describes interactions between Rydberg atoms on the ruby lattice. We leverage its local and nonlocal symmetries to determine the exact partition function and the static structure factor. A mapping between $S=3/2$ models on the honeycomb lattice and kagome spin Hamiltonians allows us to interpret the thermodynamic properties in terms of a classical kagome spin ice. Partially lifting the symmetries associated with line operators, we obtain a model characterized by immobile excitations, called classical fractons, and a ground state degeneracy that increases exponentially with the length of the system. We formulate a continuum theory that reveals the underlying gauge structure and conserved charges. Extensions of our theory to other lattices and higher-spin systems are suggested.