Corner Transfer Matrices and Quantum Affine Algebras

TL;DR

This paper explores the relationship between the corner-transfer-matrix Hamiltonian of the six-vertex model and quantum affine sl(2), proposing a conjecture about its eigenvectors forming a specific representation.

Contribution

It identifies the corner-transfer-matrix Hamiltonian as the derivation of quantum affine sl(2) and conjectures its eigenvectors form the level-1 vacuum representation.

Findings

H acts as the derivation of quantum affine sl(2)

Conjecture that eigenvectors form the level-1 vacuum representation

Supporting checks provided for the conjecture

Abstract

Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the anti-ferroelectric regime. It acts on the infinite tensor product W = V . V . V ....., where is the 2-dimensional irreducible representation of the quantum affine sl(2). We observe that H is the derivation of quantum affine sl(2), and conjecture that the eigenvectors of H form the level-1 vacuum representation of quantum affine sl(2). We report on checks in support of our conjecture.