Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations

TL;DR

This paper constructs realizations of the extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra using anyons on a 2D lattice, revealing new algebraic structures in anyonic systems.

Contribution

It introduces novel anyonic realizations of these algebras, expanding the understanding of algebraic structures in two-dimensional anyonic systems.

Findings

Realizations of extended Weyl-Heisenberg algebra using anyons

Realizations of Rubakov-Spiridonov superalgebra with anyons

Representation of $sl(1/1)$ superalgebra in an anyonic framework

Abstract

We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter $\nu\in[0,1]$, on two-dimensional lattice. The construction uses anyons defined from usual fermionic oscillators (Lerda-Sciuto construction). The anyonic realization of the superalgebra $sl(1/1)$ is also presented.