# P8: DFT for correlated nanosystems

## Project Description

Density functional theory (DFT) is very successful in the ab-initio description of electronic properties of solids. However, the predictive power is limited when one considers strongly correlated systems^{(1)} as, for example, in quantum dots and quasi one-dimensional quantum wires^{(2)}.

In order to study to which extend specific exchange-correlation potentials allow for a quantitative description of such systems, the ground-state, linear transport, and non-equilibrium properties of model systems, for example the single impurity Anderson model or the one-dimensional Hubbard model and its spinless analogon, were investigated^{(3)-(7)}. Often, one focuses on the discontinuity of the exchange-correlation potential with changing particle number^{(8)-(12), (3),(4)}. Other questions that were investigated are: What is the quality of an approximation which is local in space and time (see also P9)? Which role do dynamical corrections to the exchange-correlation potential play (see also P9)^{(13)-(15)} ? What is the functional dependence of the observables on the ground-state or time-dependent density^{(16)(17)}?

In other works the current possibilities of describing strongly correlated systems are critically analyzed^{(18)-(21)}. Here, the above mentioned three central problems in ground-state and transport DFT descriptions for zero and one-dimensional model systems as well as wires with soft-Coulomb interaction will be investigated. For these systems one can obtain either ``exact'' solutions by bosonisation^{(22),(23)}, matrix-product state based

density-matrix renormalization group (see P5 and P12), numerical renormalization group (see P10, P11, and P13) or, at least, very reliable approximations^{(2)} by functional renormalization group (see P10 and P14)^{(24)-(27)}, real-time renormalization group (see P11 and P14)^{(28)}. Comparing existing results obtained by these methods and new ones computed using RG methods with DFT calculations using known approximations we plan to extract their deficiencies which, in a second step, shall lead to improvements of the currently known approximations. First steps will contain the complete ground-state DFT description of the Anderson model (including the exchange-correlation potential in the leads^{(29)}). Also, using the time-dependent DFT description of the time evolution in the interacting resonant level model^{(30),(27),(31)}, we will analyze the question of whether a stationary

state is reached in the framework of DFT^{(5)}.

A successful DFT approach would allow for the study of realistic models for strongly correlated nanosystems, which will influence projects P10, P11, P13, P14, and P15.

(1) D. Vollhardt, Ann. Phys. (Berlin) **524**, 1 (2012)

(2) S. Andergassen, V. Meden, H. Schoeller, J. Splettstoesser and M. R. Wegewijs,

Nanotechnology **21**, 272001 (2010)

(3) N. A. Lima, M. F. Silva, L. N. Oliveira and K. Capelle, Phys. Rev. Lett.** 90**, 146402 (2003)

(4) G. Stefanucci and S. Kurth, Phys. Rev. Lett.** 107**, 216401 (2011)

(5) S. Kurth, G. Stefanucci, E. Khosravi, C. Verdozzi and E. K. U. Gross, Phys. Rev. Lett.** 104**, 236801 (2010)

(6) F. C. Alcaraz and K. Capelle, Phys. Rev. B **76**, 035109 (2007)

(7) A. Akande and S. Sanvito, J. Phys.: Condens. Matter **24**, 055602 (2012)

(8) C. O. Almbladh and U. von Barth, in *Density Functional Methods in Physics* (Plenum, New York, 1985),

pp. 209-231

(9) J. P. Perdew in *Density Functional Methods in Physics* (Plenum, New York, 1985), pp. 265-308

(10) N. Helbig, I. V. Tokatly and A. Rubio, J. Chem. Phys. **131**, 224105 (2009)

(11) O. Gunnarsson and K. Schönhammer, Phys. Rev. Lett.** 56**, 1968 (1986)

(12) K. Schönhammer, O. Gunnarsson and R. Noack, Phys. Rev. B **52**, 2504 (1995)

(13) N. Helbig, J. I. Fuks, M. Casula, M. J. Verstraete, M. A. L. Marques, I. V. Tokatly and A. Rubio,

Phys. Rev. A **83**, 032503 (2011)

(14) N. Helbig, J. I. Fuks, I. V. Tokatly, H. Appel, E. K. U. Gross and A. Rubio, Chem. Phys. **391**, 1 (2011)

(15) J. I. Fuks, N. Helbig, I. V. Tokatly and A. Rubio, Phys. Rev. B **84**, 75107 (2011)

(16) S. Kurth and G. Stefanucci, Phys. Rev. Lett.** 111**, 030601 (2013)

(17) F. Evers and P. Schmitteckert, arXiv:1308.5093

(18) P. Schmitteckert and F. Evers, Phys. Rev. Lett.** 100**, 086401 (2008)

(19) S. Schenk, M. Dzierzawa, P. Schwab and U. Eckern, Phys. Rev. B **78**, 165102 (2008)

(20) M. Dzierzawa, U. Eckern, S. Schenk and P. Schwab, Phys. Status Solidi B **246**, 941 (2009)

(21) S. Schenk, P. Schwab, M. Dzierzawa and U. Eckern, Phys. Rev. B **83**, 115128 (2011)

(22) D. Schuricht, F. H. L. Essler, A. Jaefari and E. Fradkin, Phys. Rev. Lett.** 101**, 086403 (2008)

(23) D. Schuricht, S. Andergassen and V. Meden, J. Phys.: Condens. Matter **25**, 014003 (2013)

(24) S. Andergassen, T. Enss, V. Meden, W. Metzner, U. Schollwöck and K. Schönhammer,

Phys. Rev. B **73**, 045125 (2006)

(25) C. Karrasch, T. Enss and V. Meden, Phys. Rev. B **73**, 235337 (2006)

(26) C. Karrasch, R. Hedden, R. Peters, Th. Pruschke, K. Schönhammer and V. Meden,

J. Phys.: Condens. Matter **20**, 345205 (2008)

(27) D. M. Kennes, S. G. Jakobs, C. Karrasch and V. Meden, Phys. Rev. B **85**, 085113 (2012)

(28) S. Andergassen, M. Pletyukhov, D. Schuricht, H. Schoeller and L. Borda, Phys. Rev. B **83**, 205103 (2011)

(29) G. Stefanucci and S. Kurth, Phys. Rev. Lett. **107**, 216401 (2011)

(30) C. Karrasch, S. Andergassen, M. Pletyukhov, D. Schuricht, L. Borda, V. Meden and H. Schoeller,

Europhys. Lett. **90**, 30003 (2010)

(31) D. Kennes and V. Meden, Phys. Rev. B **87**, 075130 (2013)