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The Effective Bosonic Hamiltonian for Excitons Reconsidered

M. Combescot·O. Betbeder-Matibet
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Abstract

The effective bosonic hamiltonian for excitons, extensively quoted up to now, cannot be correct because it is (surprisingly) non-hermitian. The oversight physically originates from the intrinsic difficulty of properly defining electron-hole interactions between excitons when dealing with exchange terms. By using our commutation technique, we show that the fermionic character of the excitons cannot be forced into a dressed Coulomb interaction only : The effective bosonic hamiltonian must contain purely fermionic terms of the same order as the Coulomb terms. They are necessary to ensure hermiticity, and they do not reduce to a two-body interaction, Pauli exclusion being N-body by essence.

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M. Combescot, O. Betbeder-Matibet. 2001-06-18. The Effective Bosonic Hamiltonian for Excitons Reconsidered. https://doi.org/10.1209/epl%2Fi2002-00609-3

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