Dual current anomalies and quantum transport within extended reservoir simulations

Abstract

Quantum transport simulations are rapidly evolving and now encompass well-controlled tensor network techniques for many-body transport. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts where a chemical potential or temperature drop is maintained by relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation-analog of Kramers' turnover in solution-phase chemical reactions. At intermediate relaxation, the intrinsic conductance-that given by the Landauer or Meir-Wingreen expressionsmoderates 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. The Kramers' turnover analog thus has five standard transport regimes, further constraining the parameters that lead to the intrinsic conductance. In particular, a relaxation strength proportional to the reservoir level spacing-the commonly assumed strategy-can prevent convergence to the continuum limit. This underscores that the turnover profiles enable identification of simulation parameters that achieve proper physical behavior.

The Driven Liouville von Neumann Approach to Electron Dynamics in Open Quantum Systems

“…Nonetheless, since one is forced to work with finite lead models, lead level broadening is introduced via $${{\rm{\Gamma }}}$$ to obtain an effectively continuous spectrum. The sensitivity of the transport calculation results to the tradeoff between lead dimensions and level broadening has been extensively studied [111,112,123–130] . Specifically, a typical Kramer's turnover behavior has been demonstrated for many model systems with a broad parameter stability regime [123,124,126–131] .…”

“…The sensitivity of the transport calculation results to the tradeoff between lead dimensions and level broadening has been extensively studied [111,112,123–130] . Specifically, a typical Kramer's turnover behavior has been demonstrated for many model systems with a broad parameter stability regime [123,124,126–131] . Figure 4 provides an example of the dependence of the steady‐state current on the value of the driving rate for several tight‐binding lead model sizes.…”

“…[111,112,[123][124][125][126][127][128][129][130] Specifically, a typical Kramer's turnover behavior has been demonstrated for many model systems with a broad parameter stability regime. [123,124,[126][127][128][129][130][131] Figure 4 provides an example of the dependence of the steady-state current on the value of the driving rate for several tightbinding lead model sizes. For low driving rate values, the description of the equilibrium thermal distribution in the lead models is insufficient, resulting in an underestimated current (with respect to the reference Landauer value).…”

Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach

“…5, we show the comparison of the entropy of the dot computed using our approach against the results obtained by numerically integrating the classical master equation [Eq. (50)] for increasing values of T . The plots clearly show the convergence of the results with increasing temperature, providing another benchmark for the consistency of our approach.…”

“…In this approach, the macroscopic baths are systematically approximated by a finite number of damped modes, which we call leads. Initially introduced for bosonic baths [20][21][22], this approach has been subsequently extensively used to study quantum transport in fermionic setups also [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][42][43][44][45][46][47][48][49][50][51]. When combined with tensor network techniques, it has been recently shown that it is possible to completely non-perturbatively obtain energy and particle currents in non-equilibrium steady states (NESS) of interacting quantum many-body systems, and thereby the thermodynamics at NESS, using this approach [47].…”