On the inhomogeneous T-Q relation for quantum integrable models

TL;DR

This paper extends Baxter's T-Q relation to an inhomogeneous form using the off-diagonal Bethe Ansatz, providing a new characterization of the spectrum for the periodic XXX Heisenberg spin-1/2 chain.

Contribution

It introduces an inhomogeneous T-Q relation for quantum integrable models, expanding the analytical tools for spectral analysis of such systems.

Findings

Spectrum characterized by inhomogeneous T-Q relation

Extension of Baxter's T-Q relation to inhomogeneous case

Applicable to periodic XXX Heisenberg spin-1/2 chain

Abstract

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial extension of Baxter's T-Q relation [2].