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arXiv:1011.1401 · Communications in Mathematical Physics

Exact Solution of a 2D Interacting Fermion Model

Jonas de Woul, Edwin Langmann A

Published Jul 5, 2012• 8 citations
arXivHTMLPDF
DOI
10.1007/s00220-012-1518-8

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We set up and describe in details an exact solution procedure for a 2D itinerant correlated fermionic many-body system in the presence of spin-orbit interactions, onsite Coulomb repulsion in the correlated band, and in-plane external magnetic fields.The model is non-integrable, but using the method based on positive semidefinite operator properties, exact ground states are provided below half filling, at 3/4, and above 3/4 filling.The presented technique provides the possibility to study in exact terms a 2D phenomenon with broad applicability in leading technologies. I.
We derive a low energy effective model for a two dimensional (2D) system of spinless fermions on a square lattice with repulsive short-range interactions and away from half filling. This model is a natural 2D analogue of the Luttinger model which describes interacting fermions and can be treated exactly by bosonization. It also includes fermion degrees of freedom which cannot be bosonized but, as we argue, can be treated adequately by mean field theory. Our results generalize to 2D a standard approach to 1D lattice fermion systems making them amenable to non-perturbative computation methods by a suitable continuum limit.