Bethe Ansatz for XXX chain with negative spin

TL;DR

This paper analyzes the Bethe Ansatz solution for the XXX spin chain with negative spin, revealing its connections to quantum chromodynamics, lattice nonlinear Schrödinger equation, and topological excitations, with thermodynamic and conformal field theory insights.

Contribution

It introduces the Bethe Ansatz solution for the XXX chain with negative spin and explores its physical and mathematical properties, including topological excitations and thermodynamics.

Findings

XXX chain with negative spin models QCD effective theory

Elementary excitations are fermionic lipatons as topological solitons

Provides CFT description and Yang-Yang thermodynamics for the model

Abstract

XXX spin chain with spin $s=-1$ appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger's equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy level is a scattering state of several elementary excitations [lipatons]. Lipaton is a fermion: it can be represented as a topological excitation [soliton] of original [bosonic] degrees of freedom, described by the group $Z_2$ . We also provide the CFT description (including local quenches) and Yang-Yang thermodynamics of the model.