Scalar product of twisted XXX modified Bethe vectors
S. Belliard, N. A. Slavnov, B. Vallet
TL;DR
This paper develops a modified algebraic Bethe ansatz approach to compute scalar products of Bethe vectors in twisted XXX spin chains with broken $U(1)$ symmetry, deriving an Izergin-Korepin type formula involving modified determinants.
Contribution
It introduces a new method for calculating scalar products in twisted XXX chains with broken symmetry, extending the algebraic Bethe ansatz framework.
Findings
Derived formulas for multiple actions of monodromy matrix entries
Obtained an analog of Izergin-Korepin formula for scalar products
Expressed scalar products as sums over partitions of Bethe parameters
Abstract
We consider closed XXX spin chains with broken total spin symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The obtained formulas of the multiple actions allow us to calculate the scalar products of the modified Bethe vectors. We find an analog of Izergin-Korepin formula for the scalar products. This formula involves modified Izergin determinants and can be expressed as sums over partitions of the Bethe parameters.
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