Only hybrid anyons can exist in broken symmetry phase of nonrelativistic $U(1)^{2}$ Chern-Simons theory

TL;DR

This paper explores hybrid anyons in broken symmetry phases of nonrelativistic $U(1)^2$ Chern-Simons theories, revealing their unique properties, interactions, and potential bound states.

Contribution

It introduces parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with topological vortices and analyzes the properties of hybrid anyons, including their interactions and internal structure.

Findings

Hybrid anyons are composites of one quantum of each type.

Short-range magnetic interactions can lead to bound states.

Internal structure allows for discrete energy spectra upon quantization.

Abstract

We present two examples of parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with spontaneously broken symmetry. The models possess topological vortex excitations. It is argued that the smallest possible flux quanta are composites of one quantum of each type $(1,1)$. These hybrid anyons will dominate the statistical properties near the ground state. We analyse their statistical interactions and find out that unlike in the case of Jackiw-Pi solitons there is short range magnetic interaction which can lead to formation of bound states of hybrid anyons. In addition to mutual interactions they possess internal structure which can lead upon quantisation to discrete spectrum of energy levels.