Quasiparticles in the XXZ model

TL;DR

This paper analyzes the quasiparticle structure of the XXZ model's spectrum using Bethe ansatz solutions, highlighting special cases and the evolution of quasiparticles across different regimes.

Contribution

It provides a detailed analysis of quasiparticles and their exclusion statistics in the XXZ model, including special limits like XX, XXX, and Ising, and distinguishes two types of quasiparticles.

Findings

Quasiparticles exhibit different exclusion statistics in various regimes.

Bethe ansatz string solutions evolve distinctly in planar and axial regimes.

In the Ising limit, quasiparticles become ferromagnetic domains or domain walls.

Abstract

The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX, and Ising models, where considerable simplifications occur. The XXZ spectrum can be generated from separate pseudovacua as configurations of sets of quasiparticles with different exclusion statistics. These sets are complementary in the sense that the pseudovacuum of one set contains the maximum number of particles from the other set. The Bethe ansatz string solutions of the XXX model evolve differently in the planar and axial regimes. In the Ising limit they become ferromagnetic domains with integer-valued exclusion statistics. In the XX limit they brake apart into hard-core bosons with (effectively) fermionic statistics. Two sets of quasiparticles with spin 1/2 and fractional statistics are distinguished, where one set (spinons) generates the XXZ spectrum from the unique, critical ground state realized in the planar regime, and the other set (solitons) generates the same spectrum from the twofold, antiferromagnetically ordered ground state realized in the axial regime. In the Ising limit, the solitons become antiferromagnetic domain walls.