Limitations and improvements of the relaxation time approximation in the quantum master equation: Linear conductivity in insulating systems

The nonequilibrium steady states of quantum materials have many challenges. Here, we highlight issues with the relaxation time approximation (RTA) for the dc conductivity in insulating systems. The RTA to the quantum master equation (QME) is frequently employed as a simple method, yet this phenomenological approach is exposed as containing a fatal flaw, displaying non-negligible dc conductivity in the linear response regime. We find that the puzzling behavior is caused by the fact that the density matrix in the RTA incompletely incorporates the first order of the external field. To solve this problem, we have derived a calculation scheme based on the QME that ensures correct behavior in low electric fields. Our method reproduces well the overall features of the exact electric currents in the whole field region. It is not time consuming, and its application to lattice systems is straightforward. This method will encourage progress in this research area as a simple way to more accurately describe nonequilibrium steady states.