A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian

TL;DR

This paper derives explicit ground state expressions for the two-boundary Temperley--Lieb Hamiltonian using algebraic methods, revealing a positive integral property and proposing a link to combinatorial enumeration.

Contribution

It provides explicit formulas for the ground state of the two-boundary Temperley--Lieb model and identifies a positive integral property, connecting algebraic and combinatorial aspects.

Findings

Ground state expressions explicitly derived

Ground state exhibits positive integral property

Conjectured link to enumeration of binary or permutation matrices

Abstract

We study the two-boundary Temperley--Lieb $O(n)$ loop model on Kazhdan--Lusztig bases of type A and B. We obtain explicit expressions of the ground state of the two-boundary Temperley--Lieb Hamiltonian by means of a coideal subalgebra of $U_q(\mathfrak{sl}_2)$. This ground state possesses a positive integral property. We conjecture that some components of the ground state are directly related to an enumeration of binary or permutation matrices.