Bethe Ansatz solution of triangular trimers on the triangular lattice

TL;DR

This paper presents an exact Bethe Ansatz solution for a model of triangular trimers on the triangular lattice, revealing connections to other solvable models and expanding understanding of lattice tiling problems.

Contribution

It introduces a novel exact solution for the triangular trimer model using coordinate Bethe Ansatz, linking it to related solvable lattice models.

Findings

Exact Bethe Ansatz solution for triangular trimers

Connection to square-triangle random tiling model

Discussion of relations to other solvable models

Abstract

Details are presented of a recently announced exact solution of a model consisting of triangular trimers covering the triangular lattice. The solution involves a coordinate Bethe Ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model, due to M. Widom and P. A. Kalugin. The connection of the trimer model with related solvable models is discussed.