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 (5)

• Quantum Inverse Scattering Method and Correlation Functions
• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• On correlation functions of integrable models associated to the six-vertex R-matrix
• XXZ scalar products and KP
• Factorized domain wall partition functions in trigonometric vertex models

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• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
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• Quantum integrable combinatorics of Schur polynomials
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• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Boundary one-point function of the rational six-vertex model with partial domain wall boundary conditions: explicit formulas and scaling properties
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
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• Integrable models and $K$-theoretic pushforward of Grothendieck classes