Multi-Species Anyons Supersymmetry on Two-Dimensional Space

TL;DR

This paper develops a new algebraic framework for multi-species anyons using fermions and k-fermions, constructing a fractional supersymmetry on a two-dimensional lattice.

Contribution

It introduces a redefined algebra for multi-species anyons based on fermions and k-fermions, and constructs their fractional supersymmetry on a 2D lattice.

Findings

Redefinition of multi-species anyon algebra using fermions and k-fermions

Construction of fractional supersymmetry on 2D lattice

Framework applicable to systems with different statistical parameters

Abstract

The algebra of multi-species anyons characterized by different statistical parameters $\nu_{ij}=e_{i}e_{j}\Phi_{i}\Phi_{j}/(2\pi)$, $i,j=1,...,n$ is redefined by basing on fermions and $k_{i}$-fermions ($k_{i}\in\bf{N}\rm /\{0,1\}$ with $i\in\bf{N}\rm $) and its superalgebra is constructed. The so-called fractional supersymmetry of multi-species anyons is realized on 2d lattice.