[Paper Review] Dual current anomalies and quantum transport within extended reservoir simulations

Gabriela Wójtowicz, Justin E. Elenewski+2 more|arXiv (Cornell University)|Mar 16, 2021

Quantum and electron transport phenomena101 references13 citations

TL;DR

This paper identifies dual anomalous transport regimes—virtual transitions at weak coupling and unphysical Markovian broadening at strong relaxation—within extended reservoir simulations, revealing five distinct transport regimes that challenge convergence to the intrinsic Landauer conductance. It advocates using current vs. relaxation turnover profiles to optimize simulation parameters for accurate quantum transport in open many-body systems.

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.

Motivation & Objective

• To identify and characterize anomalous transport regimes in extended reservoir simulations (ERA) for open quantum systems.
• To analyze how relaxation strength affects current convergence in matrix product state-based simulations.
• To resolve discrepancies between simulated currents and the intrinsic Landauer conductance due to unphysical broadening and virtual transitions.
• To provide a practical strategy for selecting relaxation parameters that ensure convergence to the physical continuum limit.

Proposed method

• Employs matrix product states (MPS) combined with extended reservoirs (ERA) to simulate non-equilibrium quantum transport.
• Uses a Lindblad master equation with Markovian relaxation to model reservoir coupling via time-local dissipative terms.
• Introduces a discretized reservoir with finite mode spacing and adjustable relaxation rates γ to simulate continuum behavior.
• Analyzes the current response as a function of relaxation strength to identify turnover behavior analogous to Kramers' turnover.
• Applies the Meir-Wingreen and Landauer formalisms as benchmarks for intrinsic conductance.
• Performs simulations on a single-site impurity model with tunable system-reservoir coupling and reservoir mode distribution.

Experimental results

Research questions

• RQ1 What transport regimes emerge in extended reservoir simulations when relaxation strength varies?
• RQ2 How do virtual transitions and Markovian broadening distort the current response at weak and strong relaxation?
• RQ3 Why does the common practice of setting relaxation proportional to reservoir level spacing fail to converge to the continuum limit?
• RQ4 What role does strong impurity scattering play in revealing anomalous transport behavior?
• RQ5 How can relaxation profiles be used to identify simulation parameters that recover the intrinsic conductance?

Key findings

• Five distinct transport regimes emerge in extended reservoir simulations, including two anomalous regimes: virtual transitions at weak coupling and unphysical Markovian broadening at strong relaxation.
• At weak coupling, virtual transitions lead to anomalously large currents that exceed the continuum limit, violating physical expectations.
• At strong relaxation, Markovian broadening unphysically spreads the occupied density of states, distorting the current response.
• The intrinsic conductance is only recovered when relaxation is tuned to an intermediate regime, avoiding both extreme limits.
• Choosing relaxation strength proportional to reservoir level spacing can prevent convergence to the continuum limit, undermining standard simulation practices.
• Current vs. relaxation turnover profiles provide a reliable method to identify optimal simulation parameters that reproduce physical transport behavior.