Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

Abstract

Composite structure of particles somewhat modifies their statistics, compared to the pure Boseor Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, π-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. K e y w o r d s: composite fermions (cofermions), composite bosons (cobosons, quasibosons), realization by deformed oscillators, bipartite entanglement, entanglement entropy, purity.