On Bethe strings in the two-particle sector of the closed SU(2)q invariant spin chain

TL;DR

This paper studies complex Bethe solutions in the two-particle sector of an SU(2)q invariant spin chain, comparing findings with the string conjecture and analyzing their spectral properties.

Contribution

It provides a detailed analysis of complex Bethe solutions, including their count, properties, and relation to the string conjecture in finite and thermodynamic limits.

Findings

Number of complex solutions matches conjecture predictions

Properties of solutions include spectrum position and level crossing

Connection between complex and real solutions is established

Abstract

In this paper we investigate complex solutions of the Bethe equations in the two-particle sector both for arbitrary finite number of sites and for the thermodynamic limit . We find the number of complex solutions (strings) and compare it with the string conjecture prediction. Some simple properties of these solutions like position in the spectrum, crossing of levels, connection to the ground state and transformation to the real solutions are discussed. Counting both real and complex solutions we find expected number of highest weight Bethe states.