The Effective Bosonic Hamiltonian for Excitons Reconsidered
arXiv:cond-mat/0106346 · doi:10.1209/epl/i2002-00609-3
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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