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

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

2011-04-12

arxiv.org/abs/1104.2113v1

Nucl.Phys.B852:468-507,2011

Physics

Mathematical Physics

32 pages, 24 figures

Scientific paper

10.1016/j.nuclphysb.2011.07.006

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.

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