Fractional Statistics in One-Dimension: View From An Exactly Solvable Model

TL;DR

This paper investigates one-dimensional fractional statistics using the exactly solvable Calogero-Sutherland model, deriving correlation functions and establishing the equivalence of different anyon models in the long-wavelength limit.

Contribution

It provides exact calculations of dynamical correlation functions for a 1D fractional statistics system and constructs an effective anyon model consistent with the Calogero-Sutherland model.

Findings

Correlation functions match between the ideal gas and CSM

Finite-size scaling yields correlation exponents

Evidence supports equivalence of 1D anyon models

Abstract

One-dimensional fractional statistics is studied using the Calogero-Sutherland model (CSM) which describes a system of non-relativistic quantum particles interacting with inverse-square two-body potential on a ring. The inverse-square exchange can be regarded as a pure statistical interaction and this system can be mapped to an ideal gas obeying the fractional exclusion and exchange statistics. The details of the exact calculations of the dynamical correlation functions for this ideal system is presented in this paper. An effective low-energy one-dimensional ``anyon'' model is constructed; and its correlation functions are found to be in agreement with those in the CSM; and this agreement provides an evidence for the equivalence of the first- and the second-quantized construction of the 1D anyon model at least in the long wave-length limit. Furthermore, the finite-size scaling applicable to the conformally invariant systems is used to obtain the complete set of correlation exponents for the CSM.