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Introduction Room: Sala Leonardi

Welcome

• Christian Schilling & Carlos Benavides-Riveros

Room: Sala Leonardi

Symposium 1: Exact results in RDMFT

• Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems)

Room: Sala Leonardi

DFT, RDMFT, and the challenge of strong correlations

• Eberhard Gross

Room: Sala Leonardi

Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation

• David Mazziotti

Room: Sala Leonardi

One-body Reduced Density-matrix Functional Theory for the Canonical Ensemble

• Sarina Sutter

Room: Sala Leonardi

Convex N-Representability

• Federico Castillo

Room: Sala Leonardi

Relating the pure and ensemble density matrix functional

• Christian Schilling

Room: Sala Leonardi

Implications of pinned occupation numbers for natural orbital expansions

• Tomasz Maciazek

Room: Sala Leonardi

Symposium 2: RDMFT for quantum chemistry: Computational and theoretical state-of-the-art and open challenges

• Christian Schilling (LMU Munich)

Room: Sala Leonardi

Obstacles on the road to practical implementation of RDMFT

• Jerzy Cioslowski

Room: Sala Leonardi

Global Natural Orbital Functional

• Mario Piris

Room: Sala Leonardi Appropriate representations of the electronic structure of atoms, molecules, and solids without explicit recourse to the N-particle density matrix can alternatively be obtained by the one-particle reduced density matrix (1RDM) functional theory [1]. Regrettably, computational schemes based on the exact constrained search formulation are too expensive; so the 1RDM functional requires a practical approach. For a Hamiltonian involving no more than two-body interactions, the ground-state energy can be cast as an exact functional of the two-particle reduced density matrix (2RDM). In practical applications, we employ this exact energy functional but using an approximate 2RDM that is built from the 1RDM. Approximating the energy functional has an important consequence: the functional N-representability problem arises. In this presentation, the role of the N-representability in approximate functionals [2] will be analyzed. The 1RDM functional is called Natural Orbital Functional (NOF) when it is based upon the spectral expansion of the 1RDM. So far, several approximate functionals have been proposed [3], but solely PNOFs [4,5] are based on the reconstruction of the 2RDM subject to necessary N-representability conditions. For the latter, an open source software is available [6] for quantum chemistry calculations. These functionals are capable of producing a correct description of systems with a multiconfigurational nature, however, they also suffer from an important lack of dynamic correlation. To recover this correlation, second-order perturbative corrections have been implemented with significant results [5,7]. Nevertheless, our goal is to recover the missing dynamic correlation only within the NOF theory framework. The 1RDM functional is called Natural Orbital Functional (NOF) when it is based upon the spectral expansion of the 1RDM. So far, several approximate functionals have been proposed [3], but solely PNOFs [4,5] are based on the reconstruction of the 2RDM subject to necessary N-representability conditions. For the latter, an open source software is available [6] for quantum chemistry calculations. These functionals are capable of producing a correct description of systems with a multiconfigurational nature, however, they also suffer from an important lack of dynamic correlation. To recover this correlation, second-order perturbative corrections have been implemented with significant results [5,7]. Nevertheless, our goal is to recover the missing dynamic correlation only within the NOF theory framework. In this talk, a new accurate NOF will be presented for all electronic structure problems, that is, a global NOF [8,9]. Note that the adjective "global" is used instead of "universal" to differentiate our approximate multipurpose NOF from the exact functional. The concept of the dynamic part of the occupation numbers will be introduced. The emergent functional describes the complete intrapair electron correlation and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. Different examples will be analyzed where the weak and strong electron correlations are revealed. Our results will be compared with those obtained by established accurate theoretical methods and experimental data. 1. T. L. Gilbert, Phys. Rev. B 12, 2111 (1975); M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979); S. M. Valone, J. Chem. Phys. 73, 1344 (1980). 2. M. Piris, in Many-body approaches at different scales: a tribute to N. H. March on the occasion of his 90th birthday, Chap. 22, pp. 231-247. New York: Springer (2018). 3. K. Pernal and K. J. H. Giesbertz, Top Curr Chem 368, 125-184 (2016); I. Mitxelena, M. Piris, J. M. Ugalde, Adv. Quantum Chem. 79, 155-177 (2019). 4. M. Piris, J. M. Ugalde, Int. J. Quantum Chem. 114, 1169-1175 (2014). 5. M. Piris, Phys. Rev. Lett. 119, 063002 (2017); Phys. Rev. A 98, 022504 (2018); Phys. Rev. A 100, 032508 (2019). 6. M. Piris, I. Mitxelena, Comp. Phys. Comm. 259, 107651 (2021). 7. M. Piris, X. Lopez, M. Piris, Theor. Chem. Acc. 138, 89 (2019). 8. M. Piris, “Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation”, Phys. Rev. Lett. 127, 233001 (2021). 9. I. Mitxelena, M. Piris, “Benchmarking GNOF against FCI in challenging systems in one, two and three dimensions”, J. Chem. Phys. 156, 214102 (2022). Keywords: Electron Correlation, Reduced Density Matrix Functional Theory (RDMFT), Natural Orbital Functional Theory (NOFT)

Functional-Based Description of Electronic Dynamic and Strong Correlation

• Neil Qiang Su

Room: Sala Leonardi The slow progress in systematically eliminating intrinsic errors in commonly used approximate functionals limits the applicability of functional-based descriptions to strongly correlated systems. Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT) represent two formally exact theoretical frameworks for the many-electron problem. Commonly, approximate functionals in KS-DFT and RDMFT have advantages in dealing with dynamic correlation and strong correlation, respectively. Hence, establishing a connection between both theories and developing an effective approach to combine functional approximations in both theories can create new possibilities for improving the predictive power of functional-based methods. This talk is about some effort in this direction in our group.

Towards an in-principle-exact density matrix functional embedding theory

• Emmanuel Fromager

Room: Sala Leonardi

Self-consistent-field method for correlated many-electron systems with an entropic cumulant energy

• Jian Wang

Room: Sala Leonardi Using an entropic functional for the correlation energy, an SCF method is found within the density-matrix functional theory. The method is efficient as the SCF method in Hartree-Fock or DFT theory.

Critical reassessment of recent developments in functional theory: From Hartree-Fock to i-DMFT

• Lexin Ding

Room: Sala Leonardi

Symposium 3: Extending the scope of RDMFT (Bosons, ultracold gases, and superconductors)

• Derk Kooi

Room: Sala Leonardi

Oportunities for RDMFT: Lee-Huang-Yang Fluids: from liquid droplets to supersolidity

• Alessio Recati

Room: Sala Leonardi

Reduced density matrix functional theory for bosons

• Christian Schilling

Room: Sala Leonardi

Functional theory for Bose-Einstein condensates

• Julia Liebert

Room: Sala Leonardi

Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory

• Tomasz Maciazek

Room: Sala Leonardi

Density functional theory of the superconducting state

• Eberhard Gross

Room: Sala Leonardi

Reduced density matrix functional theory for superconductors

• Carlos Benavides-Riveros

Room: Sala Leonardi

Symposium 4: conceptual aspects of RDMFT

• Jerzy Cioslowski (University of Szczecin)

Room: Sala Leonardi

New interpretation of the reduced density matrices

• Thierry Deutsch

Room: Sala Leonardi

Richardson-Gaudin Wavefunctions for Strong Correlation

• Paul Johnson

Room: Sala Leonardi Weakly-correlated systems are well-described as individual electrons. The dominant contribution to the wave function is a Slater determinant of the occupied orbitals, with small corrections from single- and double-excitations. This is not the case for strongly-correlated systems. Many Slater determinants contribute substantially and thus the correct physical picture is not independent electrons. For molecular systems, we have shown that Richardson-Gaudin (RG) states are a much better starting point. They amount to pair wave functions, but they are tractable and form a basis of the Hilbert space, allowing for systematic improvement. Pair wavefunctions are near synonymous with natural orbital functionals, and we argue that it is easier, and more reasonable physically, to consider the RG states directly.

Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT

• Sofia Bousiadi

Room: Sala Leonardi

Efficient Bosonic and Fermionic Sinkhorn Algorithms for Non-Interacting Ensembles in One-body Reduced Density Matrix Functional Theory in the Canonical Ensemble

• Derk Kooi

Room: Sala Leonardi

Relating fundamentals of functional theory: An analytic case study

• Julia Liebert

Room: Sala Leonardi

Introducing Relativistic Reduced Density Matrix Functional Theory

• Mauricio Rodriguez Mayorca

Room: Sala Leonardi

Symposium 5: Excited states, time evolution, machine learning and more

• E. K. U. Gross (The Hebrew University of Jerusalem)

Room: Sala Leonardi

Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle

• Julia Liebert

Room: Sala Leonardi

Photoemission spectra from the Extended Koopmans’ theorem: capturing weak and strong correlation

• Pina Romaniello

Room: Sala Leonardi

Machine learning for reduced density matrix functional theory

• Carlos Benavides-Riveros

Room: Sala Leonardi The one-body reduced density matrix (1RDM) plays a fundamental role in describing and predicting quantum features of bosonic and fermionic systems, such as Bose-Einstein condensation. Based on a decomposition of the 1RDM, we have developed a method to design reliable approximations for such universal functionals: Our results suggest that for translational invariant systems the constrained search approach of functional theories can be transformed into an unconstrained problem through a parametrization of a Euclidian space. This simplification of the search approach allows us to use standard machine learning methods to perform a quite efficient computation of both the universal functional and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and the quantum Monte Carlo method. This talk is based on: J. Schmidt, M. Fadel, and C. L. Benavides-Riveros, Phys. Rev. Research 3, L032063 (2021).

Diverging Exchange Force and Form of the Exact Density Matrix Functional

• Christian Schilling

Room: Sala Leonardi

Many-body energy density functional

• Giuseppina Orlandini

Room: Sala Leonardi

Closing

• Eberhard K. U. Gross (The Hebrew University of Jerusalem)
• Christian Schilling (LMU Munich)
• Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems)

Room: Sala Leonardi

Informal discussions Room: Sala Leonardi

Informal discussion Room: Sala Leonardi