Stability of the Néel quantum critical point in the presence of Dirac fermions

Abstract

We investigate the stability of the N\'eel quantum critical point of two-dimensional quantum antiferromagnets, described by a nonlinear $\ensuremath{\sigma}$ model, in the presence of a Kondo coupling to ${N}_{f}$ flavors of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using the momentum-shell renormalization group (RG), we demonstrate that the Landau damping is weakly irrelevant at the N\'eel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the N\'eel quantum critical point quasistable for ${N}_{f}\ensuremath{\ge}4$ and thermodynamically stable for ${N}_{f}<4$. In the latter case, we identify a multicritical point which describes the transition between the N\'eel critical and Kondo runaway regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multicritical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.