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Reference : UMR5626-PIELOO-003

Workplace : TOULOUSE

Date of publication : Wednesday, March 11, 2020

Scientific Responsible name : Pierre-Francois Loos and Pina Romaniello

Type of Contract : PhD Student contract / Thesis offer

Contract Period : 36 months

Start date of the thesis : 1 October 2020

Proportion of work : Full time

Remuneration : 2 135,00 € gross monthly

Multireference quasiparticle for strong correlation

This project proposes to tackle the problem of describing strong electron correlation by combining two different, yet complementary, approaches: a quantum chemistry description based on multireference wave functions (expert: Pierre-Francois Loos) and a condensed matter description based on quasiparticles (expert: Pina Romaniello), hence contemplating the concept of “multireference quasiparticles”.

Strong correlation can be nicely illustrated and understood with the simple case of the H2 molecule at dissociation: the two (antiparallel) electrons in the system localize each on one site with equal probability. In such a scenario, the (singlet) wave function of the system cannot be accurately described by a single Slater determinant, and a mean-field description would simply fail. This is not just an academic example: this kind of scenario is ubiquitous in strongly correlated materials such as NiO and, more generally, in transition metal oxides [2]. These systems exhibit remarkable electronic and magnetic properties, such as metal-insulator transitions, half-metallicity, or unconventional superconductivity, which make them among the most attractive and versatile materials with direct applications in various technological fields from nonlinear optics to sensors and catalysis. The peculiar properties of these materials origi- nates from their incompletely filled d- or f -electron shells with narrow energy bands, which require a particularly accurate theoretical treatment of electron correlation. This represents one of the greatest challenges in condensed- matter physics and quantum chemistry today.

In quantum chemistry, one usually deals directly with a complicated object (the many-body wavefunction) in order to predict and understand molecular properties

and correlation is taken into account by adding more

determinants [3]. Although systematic and black box, this

approach becomes however quickly prohibitive for large

systems. In condensed-matter physics, instead, important

formalisms such as density-functional theory and many-

body perturbation theory (MBPT) are based on simpler quantities, such as densities and Green's functions, hence avoiding the manipulation of the full many-body wave function. In particular, within the so-called GW approximation [4, 5], MBPT has become, over the last two decades, the go-to method for the calculation of quasiparticle band structures as well as direct and inverse photo-emission spectra of many materials improving substantially over the results provided by static mean-field electronic structure methods. However, GW suffers from some fundamental shortcomings, and, in particular, it is not expected to describe strong correlation [6].

In this project, we propose to merge the best of both worlds by formulating a multireference version of MBPT. This means that in situations of quasi-degenerate states, such as in the example of H2 at dissociation, one needs to define an ensemble one-body Green's function over degenerate states. During the course of the project, we propose to i) set the foundation for this new approach; ii) test the idea on simple and exactly solvable models such as the Hubbard model; iii) apply this new paradigm to real materials, such as NiO.

1F. Caruso, D. R. Rohr, M. Hellgren, X. Ren, P. Rinke, A. Rubio, and M. Scheffler, “Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory”, Phys. Rev. Lett. 110, 146403 (2013).

2S. Di Sabatino, J. A. Berger, L. Reining, and P. Romaniello, “Photoemission spectra from reduced density matrices: The band gap in strongly correlated systems”, Phys. Rev. B 94, 155141 (2016).

3(a) Y. Garniron, A. Scemama, P.-F. Loos, and M. Caffarel, “Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory”, J. Chem. Phys. 147, 034101 (2017); (b) Y. Garniron, A. Scemama, E. Giner, M. Caffarel, and P. F. Loos,

“Selected configuration interaction dressed by perturbation”, ibid. 149, 064103 (2018); (c) P. F. Loos, A. Scemama, A. Blondel, Y. Garniron, M. Caffarel, and D. Jacquemin, “A mountaineering strategy to excited states: highly-accurate reference energies and benchmarks”, J. Chem. Theory Comput. 14, 4360 (2018); (d) A. Scemama, Y. Garniron, M. Caffarel, and P. F. Loos, “Deterministic construction of nodal surfaces within quantum monte carlo: the case of FeS”, ibid. 14, 1395 (2018); (e) “Excitation energies from diffusion monte carlo using selected configuration interaction nodes”, J. Chem. Phys. 149, 034108 (2018).

4P. F. Loos, P. Romaniello, and J. A. Berger, “Green functions and self-consistency: insights from the spherium model”, J. Chem. Theory Comput. 14, 3071 (2018).

5M. Veril, P. Romaniello, J. A. Berger, and P. F. Loos, “Unphysical discontinuities in GW methods”, J. Chem. Theory Comput. 14, 5220 (2018).

6(a) P. Romaniello, S. Guyot, and L. Reining, “The self-energy beyond GW: Local and nonlocal vertex corrections”, J. Chem. Phys. 131, 154111 (2009); (b) P. Romaniello, F. Bechstedt, and L. Reining, “Beyond the GW approximation: Combining correlation channels”, Phys. Rev. B 85, 155131 (2012); (c) W. Tarantino, P. Romaniello, J. A. Berger, and L. Reining, “Self-consistent Dyson equation and self-energy functionals: An analysis and illustration on the example of the Hubbard atom”, ibid. 96, 045124 (2017).

This research project will be carried out within a collaborative project funded by the CNRS via the 80 | PRIME program (PIs: Pierre-Francois Loos, LCPQ and Pina Romaniello, LPT)

The Laboratoire de Chimie et Physique Quantiques (LCP) and the Laboratoire de Physique Theorique (LPT) à Toulouse (Université Paul Sabatier) are part of the IRSAMC Institute (physics) and is located on the campus of Paul Sabatier University.

The LCPQ and the LPT bring together more than 40 permanent researchers working in various fields of computational and theoretical chemistry and physics.

Due to the multi-disciplinary nature of the project, we encourage applications from students with a solid background in Chemistry, Physics and/or Mathematics and it is desirable that he/she is familiar with electronic structure theory and programming. During the course of this PhD project, the student will become comfortable with state-of-the-art electronic structure methods as well as simple mathematical models. He/she will also gain valuable experience in both computer algebra systems (such as MATHEMATICA) and high performance computing (HPC).

N/A

This project has received financial support from the CNRS through the 80|Prime program.

PhD scholarship in quantum chemistry/condensed matter (H/F) (TOULOUSE)
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