Triangular Trimers on the Triangular Lattice: an Exact Solution

TL;DR

This paper presents an exact solution for a model of triangular trimers on a triangular lattice, revealing the entropy of the system through a Bethe Ansatz approach, and highlighting its honeycomb structure and domain walls.

Contribution

It introduces an exactly solvable model of triangular trimers on a triangular lattice, extending dimer problem concepts with a Bethe Ansatz solution and explicit entropy calculation.

Findings

Exact entropy expression derived for the model

Model exhibits honeycomb structure with hexagonal cells

Solution employs Bethe Ansatz with two particle types

Abstract

A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated by rigid domain walls. The transfer matrix can be diagonalised by a Bethe Ansatz with two types of particles. This leads two an exact expression for the entropy on a two-dimensional subset of the parameter space.