Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models

TL;DR

This paper derives boundary conditions compatible with integrability for the six vertex and A_{n-1} models, providing explicit solutions for reflection matrices and associated Hamiltonians.

Contribution

It presents the general boundary solutions for the six vertex model and all diagonal solutions for A_{n-1} models, along with explicit integrable Hamiltonians.

Findings

General solution for six vertex boundary matrices with four parameters

All diagonal solutions for A_{n-1} boundary models

Explicit derivation of integrable magnetic Hamiltonians

Abstract

Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on four arbitrary parameters is found. For the $A_{n-1}$ models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.