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Bulletin of the American Physical Society

Nonequilibrium steady-state transport through quantum impurity models - a hybrid NRG-DMRG treatment

Frauke Schwarz, Jan von Delft, Andreas Weichselbaum

Published Mar 13, 2017• 0 citations
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The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it 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. This yields quantitatively reliable results for the current (with errors ≲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.
A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. In particular, by constructing a suitable hybrid chain, discretization errors are essentially eliminated on all time scales of interest. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength UUU. Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U1/U1/U.