Ising Fracton Spin Liquid on the Honeycomb Lattice

TL;DR

This paper investigates a classical Ising model on the honeycomb lattice, providing evidence that it exhibits a fracton spin liquid phase with unique excitations and a phase transition to a Coulomb liquid at low temperatures.

Contribution

It demonstrates the realization of a higher-rank Coulomb liquid with fracton excitations in a classical Ising model on the honeycomb lattice, and introduces a specialized Monte Carlo algorithm for studying its properties.

Findings

Evidence for a first-order transition to a fracton Coulomb phase.

Identification of membrane-like spin flip excitations and their role.

Development of a cluster Monte Carlo algorithm for defect dynamics.

Abstract

We study a classical Ising model on the honeycomb lattice with local two-body interactions and present strong evidence that at low temperature it realizes a higher-rank Coulomb liquid with fracton excitations. We show that the excitations are (type-I) fractons, appearing at the corners of membranes of spin flips. Because of the three-fold rotational symmetry of the honeycomb lattice, these membranes can be locally combined such that no excitations are created, giving rise to a set of ground states described as a liquid of membranes. We devise a cluster Monte-Carlo algorithm purposefully designed for this problem that moves pairs of defects, and use it to study the finite-temperature behavior of the model. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase whose correlations precisely match those predicted for a higher-rank Coulomb phase.