Efficient computation of the second-Born self-energy using tensor-contraction operations

Electronic transport in molecular junctions: The generalized Kadanoff-Baym ansatz with initial contact and correlations

The generalized Kadanoff-Baym ansatz (GKBA) offers a computationally inexpensive approach to simulate out-of-equilibrium quantum systems within the framework of nonequilibrium Green's functions. For finite systems, the limitation of neglecting initial correlations in the conventional GKBA approach has recently been overcome [Karlsson et al., Phys. Rev. B 98, 115148 (2018)]. However, in the context of quantum transport, the contacted nature of the initial state, i.e., a junction connected to bulk leads, requires a further extension of the GKBA approach. In this work, we lay down a GKBA scheme that includes initial correlations in a partition-free setting. In practice, this means that the equilibration of the initially correlated and contacted molecular junction can be separated from the real-time evolution. The information about the contacted initial state is included in the out-of-equilibrium calculation via explicit evaluation of the memory integral for the embedding self-energy, which can be performed without affecting the computational scaling with the simulation time and system size. We demonstrate the developed method in carbon-based molecular junctions, where we study the role of electron correlations in transient current signatures.

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is the nonequilibrium Green functions (NEGF) method. However, NEGF simulations are computationally expensive due to their T^{3} scaling with the simulation duration T. Recently, T^{2} scaling was achieved with the generalized Kadanoff-Baym ansatz (GKBA), for second-order Born (SOA) selfenergies, which has substantially extended the scope of NEGF simulations. Here we demonstrate that GKBA-NEGF simulations can be performed with order T^{1} scaling, both for SOA and GW selfenergies, and point out the remarkable capabilities of this approach.