Thermal phase transitions in a honeycomb lattice gas with three-body interactions

TL;DR

This paper investigates thermal phase transitions in a classical honeycomb lattice gas with three-body interactions, revealing first-order melting and Potts-model transitions in specific fractional filling phases.

Contribution

It provides the first detailed analysis of thermal phase transitions in a classical lattice gas with three-body interactions on the honeycomb lattice, including exact mappings and transition characterizations.

Findings

9/16 phase melts via a first-order transition

5/8 phase exhibits a four-states Potts-model transition

Ground state degeneracy reflects frustration in the system

Abstract

We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of 9/16, 5/8 and 3/4 that were identified in a previous study of a related quantum model. In particular, both the 9/16 and the 5/8 phase exhibit an extensive ground state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the 9/16 phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the 5/8 phase. Employing an exact mapping to a hard-core dimer model on an embedded honeycomb super-lattice, we find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the 5/8 phase.