Dual current anomalies and quantum transport within extended reservoir simulations

TL;DR

This paper investigates how relaxation strength affects quantum transport simulations with extended reservoirs, revealing anomalous regimes and proposing strategies to accurately reproduce intrinsic conductance.

Contribution

It identifies novel transport regimes caused by impurity scattering and relaxation effects, providing guidelines for parameter selection in extended reservoir simulations.

Findings

Weak-to-moderate relaxation reveals virtual transition effects.

Moderate-to-strong relaxation causes unphysical broadening of density states.

Turnover profiles can guide optimal simulation parameter choices.

Abstract

Quantum transport simulations are rapidly evolving and now encompass well-controlled tensor network techniques for many-body limits. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts and a chemical potential or temperature drop is maintained by external relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation analog of Kramers' turnover for solution-phase chemical reactions. At intermediate relaxation, the intrinsic conductance, that given by the Landauer or Meir-Wingreen expressions, moderates the current. We demonstrate that strong impurity scattering (i.e., a small steady-state current) reveals anomalous transport regimes within this methodology at weak-to-moderate and moderate-to-strong relaxation. The former is due to virtual transitions and the latter to unphysical broadening of the populated density of states. Thus, the turnover analog has $five$ standard transport regimes, further constraining the parameters that lead to recovery of the intrinsic conductance. In the worst case, the common strategy of choosing a relaxation strength proportional to the reservoir level spacing can prevent convergence to the continuum limit. This advocates a simulation strategy where one utilizes the current versus relaxation turnover profiles to identify simulation parameters that most efficiently reproduce the intrinsic physical behavior.