Exact finite size groundstate of the O(n=1) loop model with open boundaries

TL;DR

This paper explicitly determines the finite size groundstate of the O(n=1) loop model with open boundaries, providing exact expressions and normalization involving symplectic characters.

Contribution

It presents an explicit description of the groundstate components and normalization for the inhomogeneous transfer matrix of the O(n=1) loop model with open boundaries.

Findings

Explicit groundstate components for the model.

Exact normalization expressed as a product of symplectic characters.

Provides tools for analyzing boundary effects in loop models.

Abstract

We explicitly describe certain components of the finite size groundstate of the inhomogeneous transfer matrix of the O(n=1) loop model on a strip with non-trivial boundaries on both sides. In addition we compute explicitly the groundstate normalisation which is given as a product of four symplectic characters.