Solvable Two-Dimensional Fermion Model

Solvable Two-Dimensional Fermion Model

On a square lattice, we present a solvable spinless two-dimensional fermion model and study its integrability within the thermodynamic limit. We demonstrate that the model undergoes a metal insulator (Mott) transition within this limit. At the corresponding critical point, by using the representation theory of the q-oscillator and Weyl algebras, we show an exact mapping of the Hilbert spaces of the original model and that of a double lattice Chern-Simons theory. The essence of the transformation is further defined by the symmetry of the Quantum Group Uq(sl(2)) ⁇ Uq(sl(2)) with the parameter of deformation q = −1. This map can be regarded as an example of the implementation of the Effective Field Theory (EFT) programme, giving the Chern-Simons theory connexion as the original fermion model’s EFT. Finally, the use of the model to study soft tunnelling conductance experiments in doped semiconductors is discussed.

Author(s) Details

Federico L. Bottesi
Facultad de Ingenier´ıa y Ciencias Agrarias, Pontificia Universidad Cat´ olica Argentina, Av. Alicia Moreau de Justo 1500, (C1107AAZ) Buenos Aires, Argentina.

Guillermo R. Zemba
Facultad de Ingenier´ıa y Ciencias Agrarias, Pontificia Universidad Cat´ olica Argentina, Av. Alicia Moreau de Justo 1500, (C1107AAZ) Buenos Aires, Argentina, Departamento de F´ısica, Laboratorio Tandar, Comisi´on Nacional de Energ´ıa At´omica, Av. Libertador 8250, (C1429BNP) Buenos Aires, Argentina and Fellow of CONICET, Argentina.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/301

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