Geometry of Quantum Group invariant systems

TL;DR

This paper investigates the geometric properties of quantum group invariant systems, analyzing their metric and curvature to reveal details of anyonic behavior and stability differences compared to classical symmetries.

Contribution

It introduces a geometric framework to study quantum group invariant systems, calculating metrics and curvatures to understand their physical properties and stability.

Findings

Reveals the geometric structure of quantum group invariant systems.

Shows how anyonic behavior varies with fugacity and quantum group parameter.

Compares stability of $SU_q(2)$ systems with classical $SU(2)$ systems.

Abstract

Starting with the partition functions for quantum group invariant systems we calculate the metric in the two-dimensional space defined by the parameters $\beta$ and $\gamma=-\beta\mu$ and the corresponding scalar curvature for these systems in two and three spatial dimensions. Our results exhibit the details of the anyonic behavior of quantum group boson and fermion systems as a function of the fugacity $z$ and the quantum group parameter $q$. For the case of the quantum group $SU_q(2)$, we compare the stability of these systems with the stability of SU(2) invariant boson and fermion systems.