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

Verdozzi, Claudio LU ; Karlsson, Daniel LU ; Puig von Friesen, Marc LU ; Almbladh, Carl-Olof LU and von Barth, Ulf LU (2011) In Chemical Physics 391(1). p.37-49
Abstract
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-Schluter 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... (More)
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-Schluter 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. (C) 2011 Elsevier B. V. All rights reserved. (Less)
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organization
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type
Contribution to journal
publication status
published
subject
keywords
Linear response, Adiabatic local density approximation, Hubbard model
in
Chemical Physics
volume
391
issue
1
pages
37 - 49
publisher
Elsevier
external identifiers
  • wos:000297860500005
  • scopus:82255186454
ISSN
0301-0104
DOI
10.1016/j.chemphys.2011.04.035
language
English
LU publication?
yes
id
4ac868e9-17e4-4d09-9ec7-7af2bbb2d971 (old id 2291985)
date added to LUP
2012-01-11 15:53:50
date last changed
2017-03-19 03:59:43
@article{4ac868e9-17e4-4d09-9ec7-7af2bbb2d971,
  abstract     = {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-Schluter 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. (C) 2011 Elsevier B. V. All rights reserved.},
  author       = {Verdozzi, Claudio and Karlsson, Daniel and Puig von Friesen, Marc and Almbladh, Carl-Olof and von Barth, Ulf},
  issn         = {0301-0104},
  keyword      = {Linear response,Adiabatic local density approximation,Hubbard model},
  language     = {eng},
  number       = {1},
  pages        = {37--49},
  publisher    = {Elsevier},
  series       = {Chemical Physics},
  title        = {Some open questions in TDDFT: Clues from lattice models and Kadanoff-Baym dynamics},
  url          = {http://dx.doi.org/10.1016/j.chemphys.2011.04.035},
  volume       = {391},
  year         = {2011},
}