Laughlin type wave function for two-dimensional anyon fields in a KMS-state

TL;DR

This paper explores the correlation functions of two-dimensional anyon fields in a KMS-state, revealing that at zero temperature they resemble Laughlin wave functions, and at finite temperature they generalize this form, linking different descriptions of the fractional quantum Hall effect.

Contribution

It introduces a finite-temperature generalization of Laughlin wave functions for anyon fields in a KMS-state, connecting first and second quantized perspectives of the fractional quantum Hall effect.

Findings

At T=0, wave functions are of Laughlin type for odd level α.

At T>0, wave functions are a finite-temperature generalization of Laughlin's wave function.

The work links first and second quantized descriptions of the fractional quantum Hall effect.

Abstract

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. For T=0 the $n$-particle wave functions of noncanonical fermions of level $\alpha$, $\alpha$ odd, are shown to be of Laughlin type of order $\alpha$. For $T>0$ they are given by a simple finite-temperature generalization of Laughlin's wave function. This relates the first and second quantized pictures of the fractional quantum Hall effect.