Current anomalies, reservoir discretizations, and extended-reservoir quantum transport simulations

Quantum transport simulations are rapidly evolving, including the development of tensor network techniques for many-body calculations. One powerful approach combines matrix product states with extended reservoirs - an open system methodology where relaxation maintains a chemical potential or temperature drop. Due to the presence of external relaxation, this is a simulation analog of Kramers' turnover, with relaxation-controlled currents at both small and large relaxation strength. Only between these regimes does the natural (Landauer or Meir-Wingreen) conductance define the simulation. Here, we demonstrate how anomalous transport can appear when employing this methodology, even at moderate relaxation. While certain features are known to arise from band structure and gap states, we demonstrate that small steady-state currents unveil two anomalies, one due to virtual transitions and the other due to unphysical broadening of the occupied density of states. Moreover, we show how to approximate the optimal relaxation strength by exploiting control over the virtual anomalies, and demonstrate how reservoir discretizations impact simulation. Taken together, our results constrain the computational parameters that are needed to properly represent physical behavior in the continuum limit.