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.

32 pages, 24 figures

References in corpus (1)

• XXZ scalar products and KP

Cited by in corpus (7)

• Partial domain wall partition functions
• Colour-independent partition functions in coloured vertex models
• The SO(6) Scalar Product and Three-Point Functions from Integrability
• Slavnov determinants, Yang-Mills structure constants, and discrete KP
• Boundary one-point function of the rational six-vertex model with partial domain wall boundary conditions: explicit formulas and scaling properties
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• A duality formula between elliptic determinants