We study the nonequilibrium dynamics of small, strongly correlated clusters, described by a Hubbard Hamiltonian, by propagating in time the Kadanoff-Baym equations within the Hartree-Fock, second Born, GW, and T-matrix approximations. We compare the results to exact numerical solutions. We find that the time-dependent T matrix is overall superior to the other approximations, and is in good agreement with the exact results in the low-density regime. In the long time limit, the many-body approximations attain an unphysical steady state which we attribute to the implicit inclusion of infinite-order diagrams in a few-body system.

We present in detail a method we recently introduced ͓Phys. Rev. Lett. 103, 176404 ͑2009͔͒ to describe finite systems in and out of equilibrium, where the evolution in time is performed via the Kadanoff-Baym equations within many-body perturbation theory. Our systems consist of small, strongly correlated clusters, described by a Hubbard Hamiltonian within the Hartree-Fock, second Born, GW, and T-matrix approximations. We compare the results from the Kadanoff-Baym dynamics to those from exact numerical solutions. The outcome of our comparisons is that, among the many-body schemes considered, the T-matrix approximation is superior at low electron densities while none of the tested approximations stands out at half filling. Such comparisons permit a general assessment of the whole idea of applying many-body perturbation theory, in the Kadanoff-Baym sense, to finite systems. A striking outcome of our analysis is that when the system evolves under a strong external field, the Kadanoff-Baym equations develop a steady-state solution as a consequence of a correlation-induced damping. This damping is present both in isolated ͑finite͒ systems, where it is purely artificial, as well as in clusters contacted to ͑infinite͒ macroscopic leads. The extensive numerical characterization we performed indicates that this behavior is present whenever approximate self-energies, which include correlation effects, are used. Another important result is that, for isolated clusters, the steady state reached is not unique but depends on how one switches on the external field. When the clusters are coupled to macroscopic leads, one may reach multiple quasisteady states with arbitrarily long lifetimes. .Ϫb the GW approximation ͑GWA͒, 21 and the T-matrix approximation ͑TMA͒. 22,23 All these approximations are conserving, 1 which clearly is of great importance when propagating the KBE, and all of them, apart from HFA, have self-energies which are nonlocal in space and time. For the GWA, we will consider both a spin-independent and a spindependent version. 11,24 The latter has the advantage to alleviate the effect of self-screening. 25,26

Two aspects of TDDFT, the linear response approach and the adiabatic local density approximation, are examined from the perspective of lattice models. To this end, we review the DFT formulations on the lattice and give a concise presentation of the time-dependent Kadanoff-Baym equations, used to asses the limitations of the adiabatic approximation in TDDFT. We present results for the density response function of the 3D homogeneous Hubbard model, and point out a drawback of the linear response scheme based on the linearized Sham-Schlüter equation. We then suggest a prescription on how to amend it. Finally, we analyze the time evolution of the density in a small cubic cluster, and compare exact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results show that non-perturbative (in the interaction) adiabatic potentials can perform quite well for slow perturbations but that, for faster external fields, memory effects, as already present in simple many-body approximations, are clearly required.

PACS 71.10.-w -Theories and models of many-electron systems PACS 71.10.Fd -Lattice fermion models (Hubbard model, etc.) PACS 03.67.Mn -Entanglement measures, witnesses, and other characterizations Abstract. -We study the time-dependent transmission of entanglement entropy through an outof-equilibrium model interacting device in a quantum transport set-up. The dynamics is performed via the Kadanoff-Baym equations within many-body perturbation theory. The double occupancy n R↑nR↓ , needed to determine the entanglement entropy, is obtained from the equations of motion of the single-particle Green's function. A remarkable result of our calculations is that n R↑nR↓ can become negative, thus not permitting to evaluate the entanglement entropy. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the T -matrix approximation stands out for two reasons: it compares well to exact results in the low density regime and it always provides a non-negative n R↑nR↓ . For the second part of this statement, we give an analytical proof. Finally, the transmission of entanglement across the device is diminished by interactions but can be amplified by a current flowing through the system.Originally discussed in relation to basic aspects of quantum mechanics, entanglement is nowadays seen as a key resource for quantum information technology [1]. Solid state systems are well suited to realize quantum information devices, for their compatibility with conventional electronics hardware. This has spurred a great deal of cross-disciplinary studies on entanglement and many-body physics in the condensed phase [2].While ab-initio approaches to entanglement are starting to be explored [3,4], most studies so far have been for model systems in the ground state (see e.g. [5][6][7][8][9]). However, non-equilibrium studies are increasing in number (see e.g. [10][11][12][13]. This is because knowing how entanglement is produced/transported is pivotal for controlled quantum information manipulations, and because it can give new insight into many-body systems out of equilibrium [2].In this Letter we introduce a non-equilibrium Green's function approach to entanglement, using the timedependent Kadanoff-Baym Equations (KBE) [14,15], and computing a specific measure of entanglement, the entanglement entropy (EE) [16], within many-body perturbation theory (MBPT). The advantage of our approach is that it can be implemented ab initio [17], if one uses reliable many-body approximations (MBA:s). It is quite natural, at this point, to ask: When are MBA:s reliable to Time dependent local entanglement entropy ER and double occupancy dR, obtained within the T -matrix and the secondBorn approximations (TMA and BA, respectively) for a 7-site isolated cluster (white+red circles) with 2 particles. A perturbation vg(t) has been applied; the system parameters are U = 1, 0 = −0.5, V0 = 5, Tg = 2, bg = 0.2 (see eqs.(2-4) and main text afterwards).obtain the EE ? Here, to address this issue, we choose, as ...

We use the Kadanoff-Baym equations within the framework of many-body perturbation theory to study the double occupancies nR↑ nR↓ in a Hubbard dimer. The double occupancies are obtained from the equations of motion of the single-particle Green's function. Our calculations show that the approximate double occupancies can become negative. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the T -matrix approximation is the only one providing double occupancies which are always positive.