Eur. Phys. J. B 68, 183-192 (2009)
https://doi.org/10.1140/epjb/e2009-00087-5

Ground state energy of N Frenkel excitons

¹ Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, CNRS, Campus Boucicaut, 140 rue de Lourmel, 75015 Paris, France
² Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Izhorskaya 13/19, 125412 Moscow, Russia

Corresponding author: ^a monique.combescot@insp.jussieu.fr

Received: 16 December 2008
Published online: 14 March 2009

Abstract

By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing in the N exciton normalization factor – the cancellation being exact within terms in 1/N_s where N_s is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely appears at various stages in the precise calculation of the Hamiltonian mean value.