## Abstract

Time-resolved spectroscopy has an emerging role among modern

material-characterization techniques. Two powerful theoretical formalisms for systems out of equilibrium (and thus for time-resolved spectroscopy) are Non-Equilibrium Green’s Functions (NEGF) and Time-Dependent Density Functional Theory (TDDFT). In this chapter, we offer a perspective (with more emphasis on the NEGF) on their current capability to deal with the case of strongly correlated materials. To this end, the NEGF technique is briefly presented, and its use in time-resolved spectroscopy highlighted. We then show how a linear response description is recovered from NEGF real-time dynamics. This is followed by a review of a recent ab initio NEGF treatment and by a short introduction to TDDFT. With these background notions, we turn to the problem of describing strong correlation effects by NEGF and TDDFT. This is done in terms of model Hamiltonians: using simple lattice systems as benchmarks, we illustrate to what extent NEGF and TDDFT can presently describe complex materials out of equilibrium

and with strong electronic correlations. Finally, an outlook is given on future trends in NEGF and TDDFT research of interest to time-resolved spectroscopy.

material-characterization techniques. Two powerful theoretical formalisms for systems out of equilibrium (and thus for time-resolved spectroscopy) are Non-Equilibrium Green’s Functions (NEGF) and Time-Dependent Density Functional Theory (TDDFT). In this chapter, we offer a perspective (with more emphasis on the NEGF) on their current capability to deal with the case of strongly correlated materials. To this end, the NEGF technique is briefly presented, and its use in time-resolved spectroscopy highlighted. We then show how a linear response description is recovered from NEGF real-time dynamics. This is followed by a review of a recent ab initio NEGF treatment and by a short introduction to TDDFT. With these background notions, we turn to the problem of describing strong correlation effects by NEGF and TDDFT. This is done in terms of model Hamiltonians: using simple lattice systems as benchmarks, we illustrate to what extent NEGF and TDDFT can presently describe complex materials out of equilibrium

and with strong electronic correlations. Finally, an outlook is given on future trends in NEGF and TDDFT research of interest to time-resolved spectroscopy.

Original language | English |
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Title of host publication | First Principles Approaches to Spectroscopic Properties of Complex Materials |

Editors | Cristiana Di Valentin, Silvana Botti, Matteo Cococcioni |

Publisher | Springer |

Pages | 347-384 |

Volume | 347 |

ISBN (Print) | 978-3-642-55068-3, 978-3-642-55067-6 |

DOIs | |

Publication status | Published - 2014 |

### Publication series

Name | |
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Volume | 347 |

ISSN (Print) | 0340-1022 |

ISSN (Electronic) | 1436-5049 |

## Subject classification (UKÄ)

- Condensed Matter Physics

## Keywords

- Keywords Time-dependent spectroscopy • Strongly correlated systems • ab-initio real-time dynamics • Non-equilibrium green’s functions • TDDFT • Kadanoff– baym equations • Many-body perturbation theory • Exchange correlation potential • Self-energy