Rigged Configurations Approach For The Spin-1/2 Isotropic Heisenberg Model

TL;DR

This paper advances the analysis of solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model using rigged configurations, revealing discrete structures in complex string solutions.

Contribution

It extends rigged configurations analysis to non self-conjugate strings and counterexamples, uncovering new discrete structures in these solutions.

Findings

Identification of discrete structures in non self-conjugate strings

Analysis of counterexamples to the string hypothesis

Enhanced understanding of Bethe ansatz solutions

Abstract

We continue the rigged configurations analysis of the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model. We analyze the non self-conjugate strings of Deguchi-Giri and the counter example for the string hypothesis discovered by Essler-Korepin-Schoutens. In both cases clear discrete structures appear.