Interaction and thermodynamics of spinons in the XX chain

TL;DR

This paper explores the interaction and thermodynamics of spinons in the XX chain, revealing how their energies and couplings behave in finite and infinite systems, with implications for understanding quantum spin models.

Contribution

It provides an exact thermodynamic analysis of spinon interactions in the XX model using Bethe ansatz and describes the coupling behavior of spinons in the thermodynamic limit.

Findings

Spinon energies are expressed via Bethe ansatz equations.

Spinons exhibit Ising-like coupling that switches from ferromagnetic to antiferromagnetic.

Comparison with Haldane-Shastry model highlights similarities and differences.

Abstract

The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N -> infinity the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.