Anyonic behavior of quantum group gases

TL;DR

This paper introduces quantum group gases based on $SU_q(N)$-bosons and fermions, calculates their partition functions, and demonstrates that these gases exhibit anyonic behavior in two and three dimensions, with the parameter $q$ influencing their statistical properties.

Contribution

It presents a formalism for $SU_q(N)$-bosons and fermions, computes their grand partition functions, and shows their anyonic behavior in 2D and 3D, extending understanding of quantum group gases.

Findings

Quantum group gases exhibit anyonic behavior in 2D and 3D.

The parameter $q$ interpolates a wider range of interactions than traditional anyon parameters.

For $SU_q(2)$ boson gas at 2D, $q$ influences attractive and repulsive regimes.

Abstract

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.