Modified Algebraic Bethe Ansatz: Twisted XXX Case

TL;DR

This paper develops a modified algebraic Bethe Ansatz approach to solve the spectral problem of the twisted XXX Heisenberg spin chain with arbitrary twists and spins, introducing new basis and Baxter T-Q equations.

Contribution

It introduces a novel modified algebraic Bethe Ansatz framework for the twisted XXX chain, including two bases and two families of inhomogeneous Baxter T-Q equations.

Findings

Characterization of the spectral problem using two bases.

Derivation of two families of inhomogeneous Baxter T-Q equations.

Establishment of an inhomogeneous quantum Wronskian relation.

Abstract

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two basis to characterize the spectral problem and two families of inhomogeneous Baxter T-Q equations. The two families satisfy an inhomogeneous quantum Wronskian equation.