A solvable model of interacting fermions in two dimensions

We introduce and study an exactly solvable model of several species of ferm ions in which particles interact pairwise through a mutual magnetic held; t he interaction only operates between particles belonging to different speci es. After an unitary transformation, the model reduces to one in which each particle sees a magnetic field which depends on the total numbers of parti cles of all the other species; this may be viewed as the mean-field model f or a class of anyonic theories. Our model is invariant under charge conjuga tion 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 H all conductivity, the wavefunction overlap arising from the transfer of one particle from one species to another and the one-particle off-diagonal den sity matrix. Our model is a generalization of a recently introduced solvabl e model in one dimension.