Inhomogeneous loop models with open boundaries

TL;DR

This paper analyzes inhomogeneous dense loop models with open boundaries, deriving explicit formulas for ground state components and their sum, advancing understanding of integrable models with boundary conditions.

Contribution

It provides new Pfaffian and determinantal formulas for ground state components in inhomogeneous loop models with open boundaries, a novel analytical result.

Findings

Explicit Pfaffian and determinantal formulas derived

Ground state components computed for inhomogeneous models

Sum of components expressed in closed form

Abstract

We consider the crossing and non-crossing O(1) dense loop models on a semi-infinite strip, with inhomogeneities (spectral parameters) that preserve the integrability. We compute the components of the ground state vector and obtain a closed expression for their sum, in the form of Pfaffian and determinantal formulas.