Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model

Abstract

The (2+1)-dimensional generalized massless Thirring model with 4-component Fermi-fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector$\times$vector channel of fermion interaction with coupling constant $G_v$, the other - the scalar$\times$scalar channel with coupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearing of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. It is shown that in the particular case of pure Thirring model, i.e. at $G_s=0$, the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi-fields.