Classical $\mathbb{Z}_2$ spin liquid on the generalized four-color Kitaev model

TL;DR

This paper investigates a classical $bZ_2$ spin liquid in the four-color Kitaev model, revealing emergent gauge theory features and phase crossover behaviors through analytical and Monte Carlo methods.

Contribution

It introduces a classical $bZ_2$ spin liquid model on various lattices and characterizes its gauge and excitations properties, expanding understanding of classical spin liquids.

Findings

Identification of a classical $bZ_2$ spin liquid with emergent gauge structure

Observation of a high-to-low temperature crossover with residual entropy

Detection of $bZ_2$ flux order and diffuse spin structure factors

Abstract

While $U$(1) spin liquids have been extensively studied in both quantum and classical regimes, exact classical $\mathbb{Z}_2$ spin liquids arising from models with nearest-neighbor, bilinear spin interactions are still rare. In this Letter, we explore the four-color Kitaev model as a minimal model for stabilizing classical $\mathbb{Z}_2$ spin liquids across a broad family of tricoordinated lattices. By formulating a $\mathbb{Z}_2$ lattice gauge theory, we identify this spin liquid as being described by an emergent Gauss's law with effective charge-2 condensation, and deconfined fractionalized bond-charge excitations. We complement our findings with Monte Carlo simulations, revealing a crossover from a high-temperature paramagnet to a low-temperature liquid phase characterized by residual entropy, classical $\mathbb{Z}_2$ flux order, and diffuse spin structure factors.