Hubbard nanoclusters far from equilibrium

Abstract

The Hubbard model is a prototype for strongly correlated many-particle systems, including electrons in condensed matter and molecules, as well as for fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the nonequilibrium dynamics following a strong non-perturbative excitation only recently came into the focus of experiments and theory. It is of particular interest how the dynamics depend on the coupling strength and on the particle number and whether there exist universal features in the time evolution. Here, we present results for the dynamics of finite Hubbard clusters based on a selfconsistent nonequilibrium Green functions (NEGF) approach invoking the generalized Kadanoff--Baym ansatz (GKBA). We discuss the conserving properties of the GKBA with Hartree--Fock propagators in detail and present a generalized form of the energy conservation criterion of Baym and Kadanoff for NEGF. Furthermore, we demonstrate that the HF-GKBA cures some artifacts of prior two-time NEGF simulations. Besides, this approach substantially speeds up the numerical calculations and thus presents the capability to study comparatively large systems and to extend the analysis to long times allowing for an accurate computation of the excitation spectrum via time propagation. Our data obtained within the second Born approximation compares favorably with exact diagonalization results (available for up to 13 particles) and are expected to have predictive capability for substantially larger systems in the weak coupling limit

Toward a Nonequilibrium Green Functions Approach to Diffusion in Strongly Coupled Finite Quantum Systems

“…However, it has been shown in Ref. [27] that, even for small U , in nonequilibrium situations correlation effects may play a crucial role, in particular, for the long-time behavior. Thus, a proper many-body description requires to include correlations.…”

“…We have recently shown that these limitations can be overcome in part by employing the generalized Kadanoff Baym ansatz (GKBA) [26]. Within the second Born approximation, we could achieve long simulation times and an improved long time behavior compared to full two-time simulations, e.g., [27]. Here, we extend this approach to strong coupling by performing T-matrix calculations in combination with the GKBA.…”

“…The lowest order for the correlation selfenergy is given by the second order Born (2B) approximation. The relaxation dynamics of finite Hubbard clusters in nonequilibrium revealed [24,27,30] that the Born approximation works well for weak coupling, U 0.1. For larger coupling, the simulations have a limited time range where they are valid that shrinks as U −1 .…”

“…From the NEGF, all relevant observables can be computed [28], including the density matrix, ρ σ ss (t) = −ig σ,< ss (t, t), and the time-dependent spin density on site s, ρ σ ss (t) = n s,σ (t) ≡ n s,σ (t). The NEGF formalism provides the basis for a selfconsistent treatment of quantum, spin and correlation effects, thereby maintaining the conservation laws [29,27]. Moreover, it allows for a systematic construction of approximations via Feynman diagrams.…”

Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

“…Partial self-consistency lessened this effect. Another method related to partial self-consistency is the generalized Kadanoff-Baym ansatz (GKBA), in which one approximates certain timenondiagonal elements of the Green's function and which can be made conserving, and which is also free of artificial damping [14][15][16].…”