Europhys. Lett.
Volume 47, Number 1, July 1999
Page(s) 63 - 69
Section Condensed matter: electronic structure, electrical, magnetic and optical properties
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00352-3

Europhys. Lett, 47 (1), pp. 63-69 (1999)

Exact solution of a generalized Gross-Neveu-Thirring model

P.-A. Bares

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${\rm -w}$ - Theories and models of many electron systems.
PACS. 71.27${\rm +a}$ - Strongly correlated electron systems; heavy fermions.
PACS. 71.35${\rm -y}$ - 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 $U\rightarrow \infty$ Hubbard model, the charge excitation spectrum comprizes excitons, bi-excitons and other electron-hole complexes (droplets) for not too repulsive interactions ($-2/{\sqrt 3}\leq g\leq -1$). In the regime of strong repulsion ($g< - 2/{\sqrt 3}$), the bi-excitons and large droplets disappear from the spectrum.


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