Effects of the pseudo-Chern-Simons action for strongly correlated electrons in a plane

Abstract

Chiral symmetry breaking comes from the mass dynamically generated through interaction of Dirac fermions for both quantum electrodynamics in $(2+1)\mathrm{D}$ (QED3) and $(3+1)\mathrm{D}$ (QED4). In QED3, the presence of a Chern-Simons (CS) parameter affects the critical structure of the theory, favoring the symmetric phase where the electron remains massless. Here, we calculate the main effects of a pseudo-Chern-Simons (PCS) parameter $\ensuremath{\theta}$ into the dynamical mass generation of pseudo--quantum electrodynamics (PQED). The $\ensuremath{\theta}$ parameter provides a mass scale for PQED at the classical level and appears as the pole of the gauge-field propagator. After calculating the full electron propagator with the Schwinger-Dyson equation in the quenched-rainbow and large-$N$ approximations, we conclude that $\ensuremath{\theta}$ changes the critical parameters related to the fine-structure constant ${\ensuremath{\alpha}}_{c}(\ensuremath{\theta})$ and the number of copies of the matter field ${N}_{c}(\ensuremath{\theta})$, favoring the symmetric phase. In the continuum limit ($\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}\ensuremath{\infty}$), nevertheless, the $\ensuremath{\theta}$ parameter does not affect the critical parameters. We also compare our analytical results with numerical findings of the integral equation for the mass function of the electron. In the strong-coupling limit (with a fine-structure constant $\ensuremath{\alpha}\ensuremath{\gg}1$), the PCS mass vanishes and the system presents the same criticality as QED3.