MIRROR SYMMETRY IN THE FEW ANYON SPECTRA IN A HARMONIC OSCILLATOR POTENTIAL

TL;DR

This paper investigates mirror symmetry in the energy spectra of four and five anyons in a harmonic oscillator potential, revealing partial symmetry features similar to those in fewer anyons, but with notable differences in certain sectors.

Contribution

It demonstrates the presence of mirror symmetry in the spectra of four and five anyons, extending previous findings from fewer anyons and highlighting sector-specific symmetry breaking.

Findings

Spectra of four and five anyons show mirror symmetry about the semionic point.

The $ ext{l}=0$ sector does not exhibit mirror symmetry.

Fourth and fifth virial coefficients do not reflect the observed symmetry.

Abstract

We find that the energy spectra of four and five anyons in a harmonic potential exhibit some mirror symmetric (reflection symmetric about the semionic statistics point $\theta=\pi/2$) features analogous to the mirror symmetry in the two and three anyon spectra. However, since the $\ell=0$ sector remains non-mirror symmetric, the fourth and fifth virial coeffients do not reflect this symmetry.