## Upgrading computational approaches for many-electron ground states to higher-energy states

**Date**: Thursday February 2, 2023 - 15.00

**ONSITE**: S3 Seminar Room, third floor, Physics Department

**ONLINE**: https://tinyurl.com/StefanoPittalisColloquia

**Speaker**: Stefano Pittalis - *CNR-NANO S3*

**Title**: Upgrading computational approaches for many-electron ground states to higher-energy states

**Abstract**: Quantum excitations play an ever-increasing role in multiple and interconnected fields of fundamental and applied research. There is therefore high demand for methodologies that can model and compute excited-state properties realistically and yet efficiently. This seminar illustrates how working from ensembles instead of pure states can help to solve long-standing problems involving excitations in many-electron systems.

I will first consider the case of density functional theory (DFT). DFT is a computational framework used in tens of thousands of applicative scientific papers every year. But DFT is only defined for ground states. Ensemble-DFT (EDFT) was conceptualized with the intent of bringing cost-efficient techniques and well-developed approximations from ground state DFT to stationary excited state problems [1]. Here, I will show that enabling successful applications of EDFT involves a fundamental revision of the DFT perspective on Hartree, exchange, and correlation energies: (a) The traditional definition of Hartree and exchange energy functionals must be abandoned in favor of extended forms involving non-interacting yet multi-determinant auxiliary states [2]; (b) A new form of correlation, the so-called density-driven correlation, must also be dealt with [3]; (c) The fluctuation dissipation theorem for ensembles, allows us to break down all the novel key energy components into further elementary contributions which are amenable to well-developed or developable approximations [4]; (d) The extended density functionals must interpolate between the recently discovered high- and low-density limits for ensembles of excited states [5]. As a result, excitations which remain difficult to be tackled by (linear-response) Time-Dependent-DFT may now be computed via EDFT.

I will conclude by touching on how ensemble states can also be exploited to tackle excitations via functionals of the one-body reduced density matrix [6] and – in view of the rapid progress in quantum computing – via an extended version of the unitary coupled-cluster approach [7].

**References**:

[1] E. K. U. Gross, L. N. Oliveira, W. Kohn “Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism”, Phys. Rev. A 37 2809 (1988)

[2] T. Gould and S. Pittalis “Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster” ,Phys. Rev. Lett. 119, 243001 (2017)

[3] T. Gould and S. Pittalis “Density-Driven Correlations in Many-Electron Ensembles: Theory and Application for Excited States”, Phys. Rev. Lett. 123, 016401 (2019)

[4] T. Gould, G. Stefanucci, S. Pittalis “Ensemble density-functional theory: Insight from the fluctuation-dissipation theorem” , Phys. Rev. Lett. 125, 233001 (2020)

[5] T. Gould, D. P. Kooi, P. Gori-Giorgi, S. Pittalis “Electronic excited states in extreme limits via ensemble density functionals”, arXiv:2205.07136 (2022)

[6] C. Schilling and S. Pittalis, “Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli’s exclusion principle” Phys. Rev. Lett. 127, 023001 (2021)

[7] C.L. Benavides-Riveros, L. Chen, C. Schilling, S. Mantilla, S. Pittalis “Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach”, Phys. Rev. Lett. 129, 066401 (2022)

**Host**: Massimo Rontani (segreteria.s3@nano.cnr.it)

[Ultimo aggiornamento: 25/01/2023 13:18:15]