Nonequilibrium Green Functions Approach to Strongly Correlated Fermions in Lattice Systems

Abstract

Quantum dynamics in strongly correlated systems are of high current interest in many fields including dense plasmas, nuclear matter and condensed matter and ultracold atoms. An important model case are fermions in lattice systems that is well suited to analyze, in detail, a variety of electronic and magnetic properties of strongly correlated solids. Such systems have recently been reproduced with fermionic atoms in optical lattices which allow for a very accurate experimental analysis of the dynamics and of transport processes such as diffusion. The theoretical analysis of such systems far from equilibrium is very challenging since quantum and spin effects as well as correlations have to be treated non‐perturbatively. The only accurate method that has been successful so far are density matrix renormalization group (DMRG) simulations. However, these simulations are presently limited to one‐dimensional (1D) systems and short times. Extension of quantum dynamics simulations to two and three dimensions is commonly viewed as one of the major challenges in this field. Recently we have reported a breakthrough in this area [N. Schlünzen et al., Phys. Rev. B (2016)] where we were able to simulate the expansion dynamics of strongly correlated fermions in a Hubbard lattice following a quench of the confinement potential in 1D, 2D and 3D. The results not only exhibited excellent agreement with the experimental data but, in addition, revealed new features of the short‐time dynamics where correlations and entanglement are being build up. The method used in this work are nonequilibrium Green functions (NEGF) which are found to be very powerful in the treatment of fermionic lattice systems filling the gap presently left open by DMRG in 2D and 3D. In this paper we present a detailed introduction in the NEGF approach and its application to inhomogeneous Hubbard clusters. In detail we discuss the proper strong coupling approximation which is given by T ‐matrix selfenergies that sum up two‐particle scattering processes to infinite order. The efficient numerical implemen‐tation of the method is discussed in detail as it has allowed us to achieve dramatic performance gains. This has been the basis for the treatment of more than 100 particles over large time intervals. The numerical results presented in this paper concentrate on the diffusion in 1D to 3D lattices. We find that the expansion dynamics consist of three different phases that are linked with the build‐up of correlations. In the long time limit, a universal scaling with the particle number is revealed. By extrapolating the expansion velocities to the macroscopic limit, the obtained results show excellent agreement with recent experiments on ultracold fermions in optical lattices. Moreover we present results for the site‐resolved behavior of correlations and entanglement that can be directly compared with experiments using the recently developed atomic microscope technique. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of the dynamical collision frequency on quantum wakefields

“…This means that the result for the static electronic collision frequency from other more accurate methods (e.g. the T‐matrix approximation, , MD simulation, or density functional theory) can be used neglecting the frequency dependence, without loss of accuracy. This significantly reduces the complexity of the computation of the ion potential in streaming plasmas, e.g.…”

Time‐dependent simulation of ion stopping: Charge transfer and electronic excitations

“…[64][65][66][67] The central quantity is the one-particle [64][65][66][67] The central quantity is the one-particle…”

“…Thereto, we first generate the correlated ground state of the electrons on the lattice via an adiabatic-switching procedure, where the interaction U of the system is slowly ramped to its final value during the initial time-propagation interval (see Schlünzen and Bonitz [67] for details). We apply the NEGF approach including the GKBA, as introduced in Section 3.1, to study the coupled projectile-lattice dynamics.…”

“…A method that allows for a systematic treatment of electronic correlations in a solid-state material and, at the same time, of inhomogeneity effects induced by an external excitation are (real-time) NEGF. [64][65][66][67] The central quantity is the one-particle NEGF…”

“…We apply the NEGF approach including the GKBA, as introduced in Section 3.1, to study the coupled projectile-lattice dynamics. Thereto, we first generate the correlated ground state of the electrons on the lattice via an adiabatic-switching procedure, where the interaction U of the system is slowly ramped to its final value during the initial time-propagation interval (see Schlünzen and Bonitz [67] for details). We consider the case of U = 4 J-a configuration that allows for the build-up of correlations.…”