The many-body physics of composite bosons

Abstract

Since, up to now existing many-body theories for quantum particles were restricted to elementary fermions or elementary bosons, the treatment of interactions between composite quantum particles was only approximate. The many-body theory we describe in this Report thus constitutes a significant advance as it allows us to treat composite bosons made of two fermions as an entity, while dealing with their underlying fermionic components exactly. Pauli exclusion principle between fermions of two composite bosons appears through a set of dimensionless “Pauli scatterings” which correspond to fermion exchanges between composite bosons, in the absence of fermion interaction. In addition to these Pauli scatterings, composite bosons also have “interaction scatterings” in which composite bosons interact through the bare interactions of their elementary fermions, in the absence of fermion exchange. These two scatterings formally appear through a set of four commutators. They allow us to write any physical quantity dealing with N composite bosons in terms of these two scatterings. To visualize the physical processes which take place between composite bosons, new diagrams have been constructed. These are called “Shiva diagrams”. They explicitly show all possible fermion exchanges taking place between any number N ≥ 2 of composite bosons: this is reasonable since the Pauli exclusion principle from which they originate is N -body in essence. Shiva diagrams also are quite valuable as they allow us to readily calculate any many-body effect between N composite bosons. While these ideas can be extended to more complicated composite quantum particles, in particular to composite fermions, the present work concentrates on composite bosons made of two fermions. Up to now, we have mostly used this formalism to study semiconductor excitons: along with hydrogen atoms, excitons are the simplest of all composite bosons — just one electron and one hole with Coulomb interaction. The end of this report is dedicated to several problems dealing with excitons, to highlight how this new many-body theory can be used in practice.