Bound electron–hole pairs in semiconductors known as excitons are the subject of intense research because of their potential for optoelectronic devices and applications, especially in the realm of two-dimensional materials. While the properties of free excitons in these systems are well understood, a general description of the interactions between these quasiparticles is complicated owing to their composite nature, which leads to important exchange processes that can take place between the identical fermions of different excitons. In this work, we employ a variational approach to study interactions between Wannier excitons and obtain an effective interaction potential between two ground-state excitons in a system of spin-degenerate electrons and holes. This potential is in general nonlocal in position space and depends on the combined spin configurations of the electrons and holes. When particularized to the case of hydrogen-like excitons with a heavy hole, this potential becomes local and exactly reproduces the Heitler–London result for two interacting hydrogen atoms. Thus, our result can be interpreted as a generalization of the Heitler–London potential to the case of arbitrary masses. We also show how including corrections arising from excited states into the theory results in a van der Waals potential at large distances, which is expected given the induced dipole–dipole nature of the interactions. Our approach is also applicable to more complicated systems with nonhydrogenic exciton series, such as layered semiconductors with Rytova–Keldysh interactions. Additionally, we use a path-integral formalism to develop a many-body theory for a dilute gas of excitons, resulting in an excitonic action that formally includes many-body interactions between excitons. While in this approach the field representing the excitons is exactly bosonic, we clarify how the internal exchange processes arise in the field-theoretical treatment, and show that the diagrams corresponding to the interactions between excitons align with our variational calculation when evaluated on shell. Our methods and results lay the groundwork for a generalized theory of exciton–exciton interactions and their application to the study of biexciton spectra and correlated excitonic matter.

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• Electrostatic interactions
• Excitons
• Finite temperature field theory
• 2-dimensional systems
• Semiconductors
• Two-dimensional electron system
• Many-body techniques