A solvable model of interacting fermions in two dimensions

We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field the interaction only operates between particles belonging to different species. After an unitary transformation, the model reduces to one in which each particle sees a magnetic field which depends on the total numbers of particles of all the other species; this may be viewed as the mean-field model for a class of anyonic theories. Our model is invariant under charge conjugation C and the product PT (parity and time reversal). For the special case of two species, we examine various properties of this system, such as the Hall conductivity, the wavefunction overlap arising from the transfer of one particle from one species to another and the one-particle off-diagonal density matrix. Our model is a generalization of a recently introduced solvable model in one dimension.