Algebraic Bethe Ansatz for the FPL^2 model

TL;DR

This paper presents a simplified algebraic Bethe Ansatz method for solving the fully packed loops model with two colors, providing an alternative to the coordinate Bethe Ansatz and enabling easier analysis of the model.

Contribution

It introduces a more straightforward algebraic Bethe Ansatz approach by directly identifying the transfer matrix as a product of R-matrices, simplifying the solution process.

Findings

Derivation of Bethe equations for the FPL^2 model

Simpler algebraic approach compared to previous methods

Potential applications in related integrable models

Abstract

An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the transfer matrix is directly identified as a product of R-matrices; this allows to apply the (nested) algebraic Bethe Ansatz, which leads to the same Bethe equations. We comment on some of the applications of this result.