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.
Highlights
One approach employs a canonical transformation to a mixed basis, where energy or momentum modes are paired according to their natural scattering structure, to perform tensor network simulations that are extensive in space and time [21]
This is a substantial advance for matrix product state calculations, which are otherwise limited by the linear growth of entanglement entropy [14, 20, 22,23,24,25,26,27,28,29,30]
This broadening is responsible for the anomaly observed at moderate–to–strong relaxation strength, as well as for the zero–bias currents associated with asymmetric reservoirs [49]
Summary
The accurate simulation of many–body transport is essential to understanding nanoscale electronics and quantum dots [1,2,3], quantum dynamics and control [4,5,6,7], spintronic phenomena [8,9,10], and the development of “atomtronic” platforms for physical simulation [11,12,13,14,15,16,17,18,19,20]. One approach employs a canonical transformation to a mixed basis, where energy or momentum modes are paired according to their natural scattering structure, to perform tensor network simulations that are extensive in space and time [21]. Yond prior developments and demonstrate that additional transport regimes are unveiled for strong impurity scattering One of these is a virtual anomaly associated with tunneling processes and the other a Markovian anomaly that emerges from the unphysical Markovian broadening of the occupied density of states (DOS). Additional features can emerge due to unrelated processes (e.g., strongly off–resonant tunneling) but the five regimes we discuss appear to be universal, persisting even for weak scattering [36] and are enhanced when destructive interference is present in the impurity [65]
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