Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States

Abstract

The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group (tDMRG). This yields quantitatively reliable results for the current (with errors $\lesssim 3\%$) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.