Kadanoff-Baym equations and approximate double occupancy in a Hubbard dimer

Friesen, M. Puig von; Verdozzi, Claudio; Almbladh, Carl-Olof

doi:10.48550/arxiv.1009.2917

Cited by 4 publications

(7 citation statements)

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“…(a) to test conceptual questions of the GKBA and the numerical performance. It has been reported before that two-time NEGF simulations for small Hubbard clusters exhibit unphysical damping behavior [58]. Furthermore, approximations based on density matrices have shown numerical instabilities in the long-time regime [11].…”

Section: Results For Finite Hubbard Clustersmentioning

confidence: 95%

Hubbard nanoclusters far from equilibrium

2014

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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

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Section: Results For Finite Hubbard Clustersmentioning

confidence: 95%

Hubbard nanoclusters far from equilibrium

2014

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“…For a recent discussion of this issue we refer to Ref. [3]. To better understand the dynamics, we show the Fourier-transformed results in Figure 3.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamics of Hubbard Nano‐Clusters Following Strong Excitation

Bönitz

Hermanns

Balzer

2013

Contrib. Plasma Phys.

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The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation and relaxation dynamics following a perturbation of the system are only poorly explored. Here, we present results for the dynamics of electrons following nonlinear strong excitation that are based on a nonequilibrium Green functions approach. We focus on small systems—“Hubbard nano‐clusters”—that contain just a few particles where, in addition to the correlation effects, finite size effects and spatial inhomegeneity can be studied systematically. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Since d R is manifestly positive, this is an adverse outcome of the ALDA, and is rather general in character. Indeed, it is a long established fact that, in the RPA [120], pair correlations for the electron gas at metallic densities are strongly negative at short distances [121]; more recently, the same problem has been also experienced within the self-consistent GWA and BA [122,123].…”

Section: A Inversion Of the Non-interacting Responsementioning

confidence: 98%

“…In particular, they can be used to determine the density-density correlation function at equal times, e.g. the so-called double occupancy, nR↑ nR↓ [117,118]. However, within conserving MBA:s, correlation functions may violate important properties such as positiveness [117].…”

Section: B Some Drawbacks Of Kbe+mbptmentioning

confidence: 99%

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Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics

et al. 2011

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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.

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Kadanoff-Baym equations and approximate double occupancy in a Hubbard dimer

Cited by 4 publications

References 4 publications

Hubbard nanoclusters far from equilibrium

Hubbard nanoclusters far from equilibrium

Dynamics of Hubbard Nano‐Clusters Following Strong Excitation

Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics

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