Scalar products of Bethe vectors in the generalized algebraic Bethe ansatz
G. Kulkarni, N. A. Slavnov
TL;DR
This paper investigates scalar products of Bethe vectors in an XYZ spin chain using the generalized algebraic Bethe ansatz, providing explicit formulas especially in the free fermion case.
Contribution
It derives explicit expressions for scalar products of Bethe vectors in the XYZ spin chain, including the free fermion case, advancing understanding of their structure.
Findings
Explicit scalar product formulas in free fermion case
Generalized algebraic Bethe ansatz applied to XYZ chain
Enhanced understanding of Bethe vector interactions
Abstract
We consider an spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum many-body systems · Advanced Topics in Algebra