Spinon excitations in the XX chain: spectra, transition rates, observability

TL;DR

This paper establishes a precise mapping between lattice fermions and spinons in the XX chain, calculates transition rates, and assesses the observability of spinon excitations in the dynamic spin structure factors for various system sizes.

Contribution

It provides exact formulas for transition rates and asymptotic expressions for spinon contributions, enhancing understanding of spectral features in the XX model.

Findings

Exact mapping between Jordan-Wigner fermions and spinons for all eigenstates.

Derived formulas for transition rates using Bethe ansatz.

Assessment of spectral contribution observability for different system sizes.

Abstract

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.