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.

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