Conductivity tensor in quantum critical systems involving Dirac fermions

Dirac materials, which can be well described at low energy by Dirac fermions theories, constitute an interesting class of systems that can undergo a quantum phase transition at zero temperature, when a non-thermal parameter reaches the quantum critical point (QCP). In the vicinity of the QCP, physical observables are affected by thermal and quantum fluctuations. We study the longitudinal and Hall conductivity in a deformed Dirac fermions CFT and in the Gross-Neveu model in large N in 2+1 dimensions. We consider the effect of a detuning from the QCP and a nonzero temperature. In the large frequency regime, we show that the structure of the conductivities can be understood by using operator product expansion and conformal perturbation theory.