Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

TL;DR

This paper analyzes the spectrum and transition rates of the XX spin chain using Bethe ansatz, providing new formulas for transition rates and applying them to large chains.

Contribution

It introduces determinantal and product formulas for transition rates in the XX model and explores the Bethe ansatz solutions across the entire spectrum.

Findings

Derived explicit formulas for transition rates between Bethe states.

Applied formulas to large chains with up to 4096 sites.

Clarified the relation between quasiparticles and lattice fermions.

Abstract

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.