Dual current anomalies and quantum transport within extended reservoir simulations

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 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. 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.Comment: 16 pages, 5 figure

A GGA plus U approach to effective electronic correlations in thiolate-ligated iron-oxo (IV) porphyrin

High-valent oxo-metal complexes exhibit correlated electronic behavior on dense, low-lying electronic state manifolds, presenting challenging systems for electronic structure methods. Among these species, the iron-oxo (IV) porphyrin denoted Compound I occupies a privileged position, serving a broad spectrum of catalytic roles. The most reactive members of this family bear a thiolate axial ligand, exhibiting high activity toward molecular oxygen activation and substrate oxidation. The default approach to such systems has entailed the use of hybrid density functionals or multi-configurational/multireference methods to treat electronic correlation. An alternative approach is presented based on the GGA+U approximation to density functional theory, in which a generalized gradient approximation (GGA) functional is supplemented with a localization correction to treat on-site correlation as inspired by the Hubbard model. The electronic structure of thiolate-ligated iron-oxo (IV) porphyrin and corresponding Coulomb repulsion U are determined both empirically and self-consistently, yielding spin-distributions, state level splittings, and electronic densities of states consistent with prior hybrid functional calculations. Comparison of this detailed electronic structure with model Hamiltonian calculations suggests that the localized 3d iron moments induce correlation in the surrounding electron gas, strengthening local moment formation. This behavior is analogous to strongly correlated electronic systems such as Mott insulators, in which the GGA+U scheme serves as an effective single-particle representation for the full, correlated many-body problem

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.Comment: Manuscript + S

Open System Tensor Networks and Kramers' Crossover for Quantum Transport

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.Comment: 7 pages, 4 figure