Europhys. Lett, 47 (1), pp. 63-69 (1999)
Exact solution of a generalized Gross-Neveu-Thirring model
Institut de Physique Théorique,
École Polytechnique Fédérale de Lausanne
CH-1015 Lausanne, Switzerland
(received 16 February 1999; accepted in final form 23 April 1999)
PACS. 71.10 - Theories and models of many
PACS. 71.27 - Strongly correlated electron systems; heavy fermions.
PACS. 71.35 - Excitons and related phenomena.
We propose a model that describes approximately the strong-coupling limit of interacting electrons and holes in a one-dimensional quantum wire. An exact solution for this model at the SU(n) symmetric point of equal electron and hole masses and for a particular ratio of the forward- (f) to backward-scattering (g) is obtained by means of the Bethe ansatz. The model discussed is a hybrid between the chiral invariant Gross-Neveu model of quantum chromodynamics and the massive Thirring model. While the eigenstates exhibit a huge degeneracy in colour (spin) space as in the Hubbard model, the charge excitation spectrum comprizes excitons, bi-excitons and other electron-hole complexes (droplets) for not too repulsive interactions (). In the regime of strong repulsion (), the bi-excitons and large droplets disappear from the spectrum.
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