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An Izergin-Korepin procedure for calculating scalar products in six-vertex models

Mathematical Physics 2011-08-09 v1 High Energy Physics - Theory math.MP

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