An Izergin-Korepin procedure for calculating scalar products in six-vertex models
Abstract
Using the framework of the algebraic Bethe Ansatz, we study the scalar product of the inhomogeneous XXZ spin-1/2 chain. Inspired by the Izergin-Korepin procedure for evaluating the domain wall partition function, we obtain a set of conditions which uniquely determine the scalar product. Assuming the Bethe equations for one set of variables within the scalar product, these conditions may be solved to produce a determinant expression originally found by Slavnov. We also consider the inhomogeneous XX spin-1/2 chain in an external magnetic field. Repeating our earlier procedure, we find a set of conditions on the scalar product of this model and solve them in the presence of the Bethe equations. The expression obtained is in factorized form.
Keywords
Cite
@article{arxiv.1104.2113,
title = {An Izergin-Korepin procedure for calculating scalar products in six-vertex models},
author = {M Wheeler},
journal= {arXiv preprint arXiv:1104.2113},
year = {2011}
}
Comments
32 pages, 24 figures