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In condensed matter physics: If we describe e.g. an exciton as a combination of an electron and a hole, do we need to combine them in a Slater determinant or into a simple product state? What happens with exchange interactions?

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  • $\begingroup$ There will be a splitting between singlet and triplet states, and this normally called the exchange. But yes, I see a conceptual difficulty. The energy difference is larger in small systems (molecules, quantum dots). $\endgroup$
    – user137289
    Commented Feb 4, 2020 at 21:21

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A hole is an abstraction of a missing electron, that is of a many electron system with spin 1/2. The wave function of the total system is antisymmetric under exchange of participating electrons. This implies that there is effectively exchange interaction between the hole and electron that occupied it.

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