Reduced Density-Matrix Functional Theory: Improving its foundation

Europe/Rome
Sala Leonardi (ECT*)

Sala Leonardi

ECT*

Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
Carlos L. Benavides-Riveros (Max-Planck Institute for Complex Systems), Christian Schilling (LMU Munich), Eberhard K. U. Gross (The Hebrew University of Jerusalem)
Description

Please note that in presence attendance is by invitation only

The aim of this international workshop is to discuss and explore new aspects and challenges in
Reduced Density Matrix Functional Theory (RDMFT). For this, we invite up to 25 experts in RDMFT to
Trento for an intensive and informal meeting.

This in-person workshop during 3-14 October will be complemented by five mini-symposia (hybrid
format), open to a broad international audience:

Symposium 1 - October 3, 14:30-18:00 CEST
Exact results in RDMFT: properties of universal functionals, role of N-representability, etc.

Symposium 2 - October 5, 9:30-13:00 CEST
RDMFT for quantum chemistry: Computational and theoretical state-of-the-art and open challenges
 
Symposium 3 - October 7, 9:30-13:00 CEST
Extending the scope of RDMFT: bosons, ultracold gases, superconductors, relativistic QM, polarons,
etc.

Symposium 4 - October 10, 9:30-13:00 CEST
RDMFT for excited states and time-evolution

Symposium 5 - October 12, 9:30-13:00 CEST
RDMFT for translational invariant systems

Description

In 1959, at the Colorado conference on Molecular Quantum Mechanics, Charles Coulson pointed out that the description of atomic and molecular ground states involves the two-electron reduced density matrix (2RDM), only [1,2]. Indeed, since electrons interact only by pairwise interactions, the energies and other electronic properties of atoms and molecules can be computed directly from the 2RDM. This crucial insight has defined the starting point for the development of new theoretical approaches to the ground state problem, avoiding the use of the exponentially complex N-electron wave function. Since each subfield of the Quantum Sciences typically restricts to systems all characterized by a fixed pair interaction V (for instance Coulomb interaction in quantum chemistry, contact interaction in quantum optics and Hubbard interaction in solid state physics) the ground state problem should de facto involve only the one-particle reduced density matrix (1RDM). Indeed, for Hamiltonians of the form H(h) = h + V, where h represents the one-particle terms and V the fixed pair interaction, the conjugate variable to H(h) and h, respectively, is the 1RDM. The corresponding exact one-particle theory is known as Reduced Density Matrix Functional Theory (RDMFT) which is based on the existence of an exact energy functional of the 1RDM [3]. This interaction functional is universal in the sense that it depends only on the fixed interaction V but not on the one-particle terms h [3,4].

Most notably, compared to the widely used Density Functional Theory (DFT), RDMFT has some significant conceptual advantages and is therefore expected to overcome at some point the fundamental limitations of DFT. On the one hand, the kinetic energy is described in an exact way due to the access of the full 1RDM and all the effort can be spent to derive good approximations to the interaction energy. On the other hand, RDMFT allows explicitly for fractional occupation numbers and has therefore great prospects of describing systems with strong correlations, particularly static correlations [5]. For instance, benchmark calculations revealed that the common functionals in RDMFT yield correlation energies for closed shell atoms and molecules which are by one order of magnitude more accurate than B3LYP (one of the most popular density functionals in quantum chemistry) and a precision comparable to Møller-Plesset second-order perturbation theory [5-8]. RDMFT has also succeeded in predicting more accurate gaps of conventional semiconductors than semi-local DFT and demonstrated the insulating behavior of Mott-type insulators [9-11]. At the same time, involving the full 1RDM lies, however, also at the heart of possible disadvantages of RDMFT relative to DFT. The 1RDM involves quadratically more degrees of freedom than the spatial density and enforcing the orthonormality of the natural orbitals is computationally highly demanding [5]. Furthermore, for open-shell systems, the domain of the universal functional seems to be constrained by the more involved generalized Pauli constraints. All these aspects are still hampering RDMFT from reaching its full potential and effectiveness.

Significant recent progress on reduced density matrices and the theory of fermion correlation provides new ways for overcoming the problems of the recent realization of RDMFT. For instance, it has been observed that for many solid materials, one can exploit either the spatial locality or the translational symmetry in an efficient way, leading to more accurate functionals and remarkable additional insights [12-14]. Moreover, it has been shown that the one- and two-body N-representability constraints strongly shape the exact functional [15,16]. Due to the effort of several research groups in the world the last two years, we have witnessed a remarkable progress along several lines:

  1. In the form of the DoNOF, the first RDMFT software code has been made public just about one year ago [17].
  2. In a series of very recent works [18,19], RDMFT has been extended to excited states by generalizing the work by Gross, Oliviera and Kohn on ensemble DFT. This has revealed in particular a generalization of Pauli’s exclusion principle to mixed states [20].
  3. Novel ideas were proposed to improve the numerical minimization of functionals which may help to overcome the most severe obstacle of the recent version of RDMFT [21].
  4. RDMFT has been extended to bosonic quantum systems with remarkable new insights into its fermionic counterpart [22,23].
  5. The cusp condition due to the Coulomb interaction has finally been translated into a property of the 1RDM providing new insights into the role and accurate treatment of dynamic correlation in RDMFT [24].
  6. Quite recently, modern machine learning techniques were put forward for improving functional approximations such as in [25,26].

Most of these novel results and ideas are rather challenging, fundamental, and of potentially high impact. It will be one of the crucial challenging for the next few years to combine all those new ideas to improve the foundation of RDMFT, overcome its recent limitations and extent its scope by including also non-singlet, finite-temperature, and time-evolving systems [27,28].

Bibliography

[1] C. A. Coulson, “Present state of molecular structure calculations”, Rev. Mod. Phys. 32, 170 (1960).
[2] D. A. Mazziotti (ed.), Reduced Density-Matrix mechanics: with applications to many-electron atoms and molecules, John Wiley & Sons (2007).
[3] T. L. Gilbert, “Hohenberg-Kohn theorem for nonlocal external potentials”, Phys. Rev. B 12, 2111 (1975).
[4] M. Levy, “Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem”, PNAS 76, 6062 (1979).
[5] K. Pernal and K. J. Giesbertz, “Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT)”, Top. Curr. Chem. 368, 125 (2016).
[6] N. Lathiotakis and M. A. L. Marques, “Benchmark calculations for reduced density-matrix functional theory”, J. Chem. Phys. 128, 184103 (2008).
[7] M. Piris, “A natural orbital functional based on an explicit approach of the two-electron cumulant”, Int. J. Quantum Chem. 113, 620 (2012).
[8] M. Piris, “Global Method for Electron Correlation”, Phys. Rev. Lett. 119, 063002 (2017).
[9] S. Sharma, J. K. Dewhurst, S. Shallcross, and E. K. U. Gross, “Spectral Density and Metal-Insulator Phase Transition in Mott Insulators Within Reduced Density Matrix Functional Theory”, Phys. Rev. Lett. 110, 116403 (2013).
[10] Y. Shinohara, S. Sharma, J. K. Dewhurst, S. Shallcross, N. N. Lathiotakis, and E. K. U. Gross, “Doping induced metal-insulator phase transition in NiO. A reduced density matrix functional theory perspective”, New J. Phys. 17, 093038 (2015).
[11] K. Pernal, “Turning reduced density matrix theory into a practical tool for studying the Mott transition”, New J. Phys. 17, 111001 (2015).
[12] M. Saubanère, M. B. Lepetit, and G. M. Pastor, “Interaction-energy functional of the Hubbard model: Local formulation and application to low-dimensional lattices”, Phys. Rev. B 94, 045102 (2016).
[13] C. Schilling and R. Schilling, “Diverging exchange force and form of the exact density matrix functional”, Phys. Rev. Lett. 122, 013001 (2019).
[14] J. Schmidt, C. L. Benavides-Riveros, and M. A. L. Marques, “Reduced density matrix functional theory for superconductors”, Phys. Rev. B 99, 224502 (2019).
[15] M. Piris, “The Role of the N-Representability in One-Particle Functional Theories”, chapter in “Many-body Approaches at Different Scales” (Springer, New York, 2016) Chapter 22.
[16] C. Schilling, “Communication: Relating the pure and ensemble density matrix functional”, J. Chem. Phys. 149, 231102 (2018).
[17] M. Piris, I. Mitxelena, Comput. Phys. Commun. 259, 107651 (2021).
[18] C. Schilling, S. Pittalis, Phys. Rev. Lett. 127, 023001 (2021)
[19] J. Liebert, F. Castillo, J.-P. Labbé, C. Schilling, arXiv:2106.03918, to appear in J. Chem. Theory Comput.
[20] F. Castillo, J.-P. Labbé, J. Liebert, A.Padrol, E.Philippe, C. Schilling, arXiv:2105.06459
[21] D. Gibney, J.N. Boyn, D.A. Mazziotti, J. Phys. Chem. Lett. 12, 385 (2021)
[22] C.L. Benavides-Riveros, J. Wolff, M.A.L. Marques, C. Schilling, Phys. Rev. Lett. 124, 180603 (2020)
[23] J. Liebert, C. Schilling, Phys. Rev. Research 3, 013282 (2021)
[24] J. Cioslowski, J. Chem. Phys. 153, 154108 (2020)
[25] J. Schmidt, C.L. Benavides-Riveros, and M.A.L. Marques, J. Phys. Chem. Lett. 10, 6425 (2019)
[26] J. Schmidt, M. Fadel, C.L. Benavides-Riveros, Phys. Rev. Research 3, L032063 (2021).
[27] K. Giesbertz, O. Gritsenko, and E. Baerends, “Response calculations with an independent particle system with exact one-particle density matrix”, Phys. Rev. Lett. 105, 013002 (2010).
[28] K. Giesbertz and M. Ruggenthaler, “One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures”, Phys. Rep. 806, 1 (2019).
Participants
  • Abdeslam HOUARI
  • Alessio Recati
  • Alfonso Gallo
  • Amir Mofrad
  • Ashima Ashima
  • Ashok Singh Ashok Singh
  • Bastiaan Braams
  • Brajesh Rajesh Bhagat
  • Carlos Benavides-Riveros
  • Cheng-Lin Hong
  • Christian Schilling
  • Damiano Aliverti
  • Daniel Gibney
  • David Mazziotti
  • Derk Kooi
  • Dhirendra Mishra
  • Dirk Andrae
  • Divya Prakash Rai
  • E.K.U. Gross
  • Ehsan Barati
  • Emmanuel Fromager
  • Federico Castillo
  • Gergely Juhasz
  • Gesa Dünnweber
  • Giuseppina Orlandini
  • Isaac Leonardo Huidobro-Meezs
  • Javier Faba
  • Jean Baptiste Fankam Fankam
  • Jerzy Cioslowski
  • Jian Wang
  • Julia Liebert
  • Jun Huang
  • Kaustav Chatterjee
  • Kesha Sorathia
  • Khaled DINE
  • Kiran kumar Atyam
  • Lexin Ding
  • Luis Colmenarez
  • Luis Vasquez
  • Lukas Kienesberger
  • Mabel Moreno
  • Mahendiran Durairaj
  • Mario Piris
  • Martina Jung
  • Mauricio Rodríguez Mayorga
  • Md. Sakibul Islam
  • Mihir Ranjan Sahoo
  • MOHD USSAMA
  • monika rani
  • Munavvar Husain
  • Neil Qiang Su
  • Nicholas Lee
  • Nicolas Cartier
  • Paul Johnson
  • Pierre-Francois LOOS
  • Pina Romaniello
  • Prateek Jain
  • Priyanka Kumari
  • Radu Isai
  • Raul QUINTERO
  • Raymundo Vazquez Martinez
  • Reinaldo Pis Diez
  • Robert Lavroff
  • Robert Schade
  • Rodrigue CHABI DOCO
  • Rohit Sathe
  • Sangeeta .
  • Saptarshi Ghosh Dastider
  • Sarina Sutter
  • Sayed Razee
  • Shibu Meher
  • Simen Kvaal
  • SIVASAKTHI P
  • Sofia Bousiadi
  • Sreejith Pallikkara Chandrasekharan
  • sunil kumawat
  • Tahir wahab
  • TANMAY THAKUR
  • Thierry Deutsch
  • Tomasz Maciazek
  • Tomoya Naito
  • Xiaowei Sheng
  • Xiaowei Xie
  • Yangyi Lu
  • Yihan Hu
Videoconference
Reduced Density-Matrix Functional Theory
Zoom Meeting ID
86885690701
Host
Susan Driessen
Zoom URL
Susan Driessen
    • 10:00 10:30
      Registration 30m Hall Rustico

      Hall Rustico

    • 10:30 11:00
      Introduction 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m
    • 11:30 13:00
      Welcome 1h 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Christian Schilling & Carlos Benavides-Riveros
    • 13:00 14:29
      Lunch 1h 29m
    • 14:29 14:30
      Symposium 1: Exact results in RDMFT 1m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems)
    • 14:30 15:00
      DFT, RDMFT, and the challenge of strong correlations 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Eberhard Gross
    • 15:00 15:30
      Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: David Mazziotti
    • 15:30 16:00
      One-body Reduced Density-matrix Functional Theory for the Canonical Ensemble 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Sarina Sutter
    • 16:00 16:30
      Coffee break 30m
    • 16:30 17:00
      Convex N-Representability 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Federico Castillo
    • 17:00 17:30
      Relating the pure and ensemble density matrix functional 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Christian Schilling
    • 17:30 18:00
      Implications of pinned occupation numbers for natural orbital expansions 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Tomasz Maciazek
    • 09:30 11:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m
    • 11:30 13:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 16:30 18:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:29 09:30
      Symposium 2: RDMFT for quantum chemistry: Computational and theoretical state-of-the-art and open challenges 1m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Christian Schilling (LMU Munich)
    • 09:30 10:00
      Obstacles on the road to practical implementation of RDMFT 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Jerzy Cioslowski
    • 10:00 10:30
      Global Natural Orbital Functional 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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)

      Speaker: Mario Piris
    • 10:30 11:00
      Functional-Based Description of Electronic Dynamic and Strong Correlation 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Neil Qiang Su
    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:00
      Towards an in-principle-exact density matrix functional embedding theory 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Emmanuel Fromager
    • 12:00 12:30
      Self-consistent-field method for correlated many-electron systems with an entropic cumulant energy 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Jian Wang
    • 12:30 13:00
      Critical reassessment of recent developments in functional theory: From Hartree-Fock to i-DMFT 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Lexin Ding
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 16:30 18:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 19:30 21:30
      Dinner (Ristorante Ca dei Gobj) 2h Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      Via del Simonino, 14, 38122 Trento TN

    • 09:30 11:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m
    • 11:30 13:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 16:30 18:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:29 09:30
      Symposium 3: Extending the scope of RDMFT (Bosons, ultracold gases, and superconductors) 1m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Derk Kooi
    • 09:30 10:00
      Oportunities for RDMFT: Lee-Huang-Yang Fluids: from liquid droplets to supersolidity 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Alessio Recati
    • 10:00 10:30
      Reduced density matrix functional theory for bosons 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Christian Schilling
    • 10:30 11:00
      Functional theory for Bose-Einstein condensates 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Julia Liebert
    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:00
      Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Tomasz Maciazek
    • 12:00 12:30
      Density functional theory of the superconducting state 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Eberhard Gross
    • 12:30 13:00
      Reduced density matrix functional theory for superconductors 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Carlos Benavides-Riveros
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 09:29 09:30
      Symposium 4: conceptual aspects of RDMFT 1m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Jerzy Cioslowski (University of Szczecin)
    • 09:30 10:00
      New interpretation of the reduced density matrices 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Thierry Deutsch
    • 10:00 10:30
      Richardson-Gaudin Wavefunctions for Strong Correlation 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Paul Johnson
    • 10:30 11:00
      Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Sofia Bousiadi
    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:00
      Efficient Bosonic and Fermionic Sinkhorn Algorithms for Non-Interacting Ensembles in One-body Reduced Density Matrix Functional Theory in the Canonical Ensemble 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Derk Kooi
    • 12:00 12:30
      Relating fundamentals of functional theory: An analytic case study 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Julia Liebert
    • 12:30 13:00
      Introducing Relativistic Reduced Density Matrix Functional Theory 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Mauricio Rodriguez Mayorca
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 16:30 17:30
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:30 11:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m
    • 11:30 13:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 16:30 17:30
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:25 09:26
      Symposium 5: Excited states, time evolution, machine learning and more 1m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: E. K. U. Gross (The Hebrew University of Jerusalem)
    • 09:30 10:00
      Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Julia Liebert
    • 10:00 10:30
      Photoemission spectra from the Extended Koopmans’ theorem: capturing weak and strong correlation 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Pina Romaniello
    • 10:30 11:00
      Machine learning for reduced density matrix functional theory 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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).

      Speaker: Carlos Benavides-Riveros
    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:00
      Diverging Exchange Force and Form of the Exact Density Matrix Functional 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Christian Schilling
    • 12:00 12:30
      Many-body energy density functional 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Giuseppina Orlandini
    • 12:30 13:00
      Closing 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speakers: Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems), Christian Schilling (LMU Munich), Eberhard K. U. Gross (The Hebrew University of Jerusalem)
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 19:30 21:30
      Dinner 2h Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:30 11:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m
    • 11:30 13:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 13:00 14:30
      Lunch 1h 30m
    • 14:30 16:00
      INFORMAL DISCUSSIONS Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00 16:30
      Coffee break 30m
    • 09:30 11:00
      Informal discussions 1h 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:00 11:30
      Coffee break 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11:30 13:00
      Informal discussion 1h 30m Sala Leonardi

      Sala Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 13:00 14:30
      Lunch 1h 30m