Entanglement entropy of composite fermions realized by (deformed) fermions vs. that of composite bosons

Abstract

In our two preceding papers we studied bipartite composite boson (or quasiboson) systems through their realization in terms of deformed oscillators. Therein, the entanglement characteristics such as the entanglement entropy and purity were found and expressed, for both one-quasiboson and more complex states, through the parameter of deformation. In this work we initiate an analogous study of composite fermions for two major cases: (i) "boson + fermion" composites; (ii) "deformed-boson + fermion" composites. Both the entanglement entropy and purity of composite fermions are dealt with, their dependence on the relevant parameters established, and for some particular two- or three-mode cases depicted graphically. In a few special cases the entanglement entropy turns out to be constant $S_0=\ln 2$ (or $\ln 3$) or $S_0=0$, while in the rest of the cases which we considered it varies between zero and $\ln 2$ (or $\ln 3$).