Exchange statistics in 1D: from the viewpoint of exact solution

TL;DR

This paper demonstrates that exchange statistics significantly influence 1D systems with compact topology, providing exact calculations of partition functions and correlators for free q-particles and a spin 1/2 XY-chain.

Contribution

It reveals the non-trivial effects of exchange statistics in 1D systems with compact topology and offers exact solutions for specific models.

Findings

Exchange statistics affect 1D systems with compact topology.

Exact partition function and correlator calculations for free q-particles.

Analysis of a spin 1/2 XY-chain with periodic boundary conditions.

Abstract

We show that the exchange statistics have consequences in 1D systems with compact topology, contrary to the common opinion that exchange statistics is arbitrary in 1D. As examples of non-trivial statistical behavior we exactly calculate the partition function and correlators for systems of free q-particles on compactified chains using functional integral techniques and the supersymmetric trick. In particular we consider a spin 1/2 XY-chain with periodic boundary conditions that corresponds to the case of q=-1.