Statistically interacting quasiparticles in Ising chains

TL;DR

This paper explores the exclusion statistics of quasiparticles in Ising chains with spins 1/2 and 1, revealing their thermodynamic behavior and connections to other models like the XXZ chain.

Contribution

It identifies and characterizes the exclusion statistics of quasiparticles in Ising chains, including solitons and strings, and relates their thermodynamics to known models.

Findings

Exact thermodynamic analysis of domain systems up to size M

Equivalence of large M limit to the s=1/2 Ising chain thermodynamics

Relation between Ising solitons and XX spinons

Abstract

The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s=1/2,1. In the s=1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s=1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s=1/2 and to a system of six species of soliton pairs for s=1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to $M$ lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M -> infinity, to the thermodynamics of the s=1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s=1/2 XXZ chain.