Partition function of the trigonometric SOS model with reflecting end

TL;DR

This paper derives a determinant representation for the partition function of the trigonometric SOS model with a reflecting boundary, facilitating the analysis of Bethe vectors in spin chains with non-diagonal boundaries.

Contribution

It provides a new single Izergin determinant formula for the partition function with reflecting end, extending previous determinant sums for models without reflection.

Findings

Partition function expressed as a single Izergin determinant.

Facilitates analysis of Bethe vectors in non-diagonal boundary spin chains.

Extends determinant formulas to models with reflecting boundaries.

Abstract

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.