Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

TL;DR

This paper investigates the wavefunctions and entanglement properties of composite fermions modeled as deformed oscillators, extending previous work on composite bosons to include fermionic and mixed cases, revealing how entanglement measures depend on deformation parameters.

Contribution

It introduces a framework for describing composite fermions as deformed oscillators and analyzes their entanglement characteristics, expanding the understanding of particle statistics modifications.

Findings

Composite fermions can be modeled as deformed oscillators with specific wavefunctions.

Entanglement entropy and purity are explicitly calculated for different composite fermion cases.

Graphical illustrations show how entanglement measures vary with deformation parameters.

Abstract

Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and, likewise, baryons are not pure fermions. In our preceding papers, we studied bipartite composite boson (i.e. quasiboson) systems via a realization by deformed oscillators. Therein, the interconstituent entanglement characteristics such as entanglement entropy and purity were found in terms of the parameter of deformation. Herein, we perform an analogous study of composite Fermi-type particles, and explore them in two major cases: (i) "boson + fermion" composite fermions (or cofermions, or CFs); (ii) "deformed boson + fermion" CFs. As we show, cofermions in both cases admit only the realization by ordinary fermions. Case (i) is solved explicitly, and admissible wavefunctions are found along with entanglement measures. Case (ii) is treated within few modes both for CFs and constituents. The entanglement entropy and purity of CFs are obtained via the relevant parameters and illustrated graphically.