Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings

TL;DR

This paper investigates the classical Heisenberg spins with Kitaev interactions on a hexagonal lattice, revealing a highly degenerate ground state manifold, a solid-on-solid model analogy, and decay of correlations, supported by Monte Carlo simulations.

Contribution

It introduces a detailed analysis of the classical Heisenberg-Kitaev model on a hexagonal lattice, highlighting the ground state degeneracy and correlation decay, and relates it to quantum models.

Findings

Ground states form an (N+1)-dimensional manifold.

Bond-energy correlations decay as 1/R^2.

Monte Carlo simulations verify correlation decay.

Abstract

We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbour interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order-by-disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R^2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin-S Kitaev model for large S, and obtain lower and upper bounds on the ground state energy of the quantum model.