Ground state solutions of inhomogeneous Bethe equations

TL;DR

This paper investigates the distribution of Bethe roots in the ground state of the inhomogeneous XXX Heisenberg spin chain, showing the inhomogeneous term's negligible effect in the thermodynamic limit and analyzing root behaviors.

Contribution

It provides new insights into the ground state solutions of inhomogeneous Bethe equations and validates conjectures about Bethe root behaviors for large system sizes.

Findings

Inhomogeneous term does not affect the Baxter T-Q equation in the thermodynamic limit.

Identifies and classifies different families of Bethe roots.

Conjectures and validates large N behavior of Bethe roots.

Abstract

The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated. Numerical calculations shows that, for this state, the new inhomogeneous term does not contribute to the Baxter T-Q equation in the thermodynamic limit. Different families of Bethe roots are identified and their large N behaviour are conjectured and validated.