Deformed strings in the Heisenberg model

TL;DR

This paper explores complex, deformed string solutions in the Bethe equations for the Heisenberg chain, extending traditional models by including generic deformations and analyzing their implications for eigenstates and correlation functions.

Contribution

It introduces a general method to construct eigenstates with deformed strings, surpassing the traditional undeformed string hypothesis, and analyzes their properties and contributions.

Findings

Deformed strings can be systematically constructed for the Heisenberg model.

Explicit solutions for short chains demonstrate the method's effectiveness.

Certain singular solutions do not contribute to zero-temperature correlations.

Abstract

We investigate solutions to the Bethe equations for the isotropic S = 1/2 Heisenberg chain involving complex, string-like rapidity configurations of arbitrary length. Going beyond the traditional string hypothesis of undeformed strings, we describe a general procedure to construct eigenstates including strings with generic deformations, discuss general features of these solutions, and provide a number of explicit examples including complete solutions for all wavefunctions of short chains. We finally investigate some singular cases and show from simple symmetry arguments that their contribution to zero-temperature correlation functions vanishes.