Off-shell scalar products for the $XXZ$ spin chain with open boundaries

Abstract

In this work we study scalar products of Bethe vectors associated with the $XXZ$ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products through functional relations follows from a particular map having the reflection algebra as its domain and a function space as the codomain. Within this approach we find a multiple contour integral representation for the scalar products in which the homogeneous limit can be obtained trivially.

arXiv comment33 pages. v2: figure and references added, presentation slightly modified

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Cited by in corpus (8)

• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• New differential equations in the six-vertex model
• Quantum-classical duality for Gaudin magnets with boundary
• The Functional Method for the Domain-Wall Partition Function
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Differential approach to on-shell scalar products in six-vertex models
• Continuous representations of scalar products of Bethe vectors
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary