Performance of Reservoir Discretizations in Quantum Transport Simulations

Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers' turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that a given reservoir discretization may have little impact on numerical efficiency for certain computational tools. The choice of a relaxation parameter, however, is crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.