Linear response time-dependent density functional theory of the Hubbard dimer
Abstract
The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. In conclusion, many exact results, limits, and expansions about those limits are given in the Appendices.
- Authors:
-
- Univ. de Oviedo, Oviedo (Spain); Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Nanomaterials and Nanotechnology Research Center
- City Univ. of New York (CUNY), NY (United States)
- Univ. of California, Irvine, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Irvine, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
- OSTI Identifier:
- 1595120
- Alternate Identifier(s):
- OSTI ID: 1866807
- Grant/Contract Number:
- FG02-08ER46496; FIS2012-34858
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Physical Journal. B, Condensed Matter and Complex Systems
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 7; Journal ID: ISSN 1434-6028
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, and Burke, Kieron. Linear response time-dependent density functional theory of the Hubbard dimer. United States: N. p., 2018.
Web. doi:10.1140/epjb/e2018-90114-9.
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, & Burke, Kieron. Linear response time-dependent density functional theory of the Hubbard dimer. United States. https://doi.org/10.1140/epjb/e2018-90114-9
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, and Burke, Kieron. Mon .
"Linear response time-dependent density functional theory of the Hubbard dimer". United States. https://doi.org/10.1140/epjb/e2018-90114-9. https://www.osti.gov/servlets/purl/1595120.
@article{osti_1595120,
title = {Linear response time-dependent density functional theory of the Hubbard dimer},
author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
abstractNote = {The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. In conclusion, many exact results, limits, and expansions about those limits are given in the Appendices.},
doi = {10.1140/epjb/e2018-90114-9},
journal = {European Physical Journal. B, Condensed Matter and Complex Systems},
number = 7,
volume = 91,
place = {United States},
year = {Mon Jul 02 00:00:00 EDT 2018},
month = {Mon Jul 02 00:00:00 EDT 2018}
}
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