Solvable Two-Dimensional Fermion Model

Abstract

We present a solvable spinless two-dimensional fermion model on a square lattice and analyze itsintegrability in the thermodynamic limit. We show that in this limit the model undergoes a metal-insulator (Mott) transition. At the corresponding critical point we exhibit an exact mapping betweenthe Hilbert spaces of the original model and that of a double lattice Chern-Simons theory by usingthe representation theory of the q-oscillator and Weyl algebras. The nature of the transition is furthercharacterized by the Quantum Group symmetry Uq(sl(2)) ⊗ Uq(sl(2)) with deformation parameterq = −1. This map may be considered as an example of the realization of the Effective Field Theory(EFT) program, yielding the association of the Chern-Simons theory as the EFT of the originalfermion model. Finally, we discuss the application of the model for the study of tunneling conductanceexperiments in doped semiconductors.