From 6d3d95372b9bd922011a2f5d24caf4118529233b Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 7 Nov 2023 15:01:30 +0100 Subject: [PATCH] modifs presentation --- content/presentations.md | 128 ++++++++++++++++++++------------------- 1 file changed, 65 insertions(+), 63 deletions(-) diff --git a/content/presentations.md b/content/presentations.md index 06d906c..f4c8621 100644 --- a/content/presentations.md +++ b/content/presentations.md @@ -66,45 +66,12 @@ in first quantization, we develop an effective QED Hamiltonian in a fermionic Fo **TBA** -### Leo Gaspard (LCPQ, Toulouse) - -**Application of DMFT to realistic materials : the example of Ba2IrO4** - -Describing the behavior of strongly correlated materials from first principles remains nowadays a challenge in computational condensed matter physics. Indeed, when Coulomb interaction is of the same order of magnitude as the kinetic energy of the electrons, like in materials with open d-shells, the Kohn-Sham band structure obtained within Density Functional Theory (DFT) is often quantitatively -- and even sometimes qualitatively -- wrong. To take strong correlations into account, Dynamical Mean Field Theory (DMFT) has been successfully coupled with DFT, in a scheme dubbed DFT+DMFT, to treat such systems for the past 25 years [1,2]. - -In this talk, I will introduce how the state-of-the-art DFT+DMFT calculations can be performed, using the example of Ba2IrO4, a compound isostructural to the well-known La2CuO4 [3]: starting from a DFT calculation, a Hubbard-Kanamori-like model Hamiltonian is parametrized [4,5] using Wannier functions [6] and constrained Random Phase Approximation (cRPA) [7]. The model is then solved within DMFT using a continuous time Monte-Carlo solver in the Hybridization expansion (CT-HYB) scheme [8]. The calculated spectral function compares very well with available experimental angle-resolved photo-emission spectroscopy (ARPES) data [3] and sheds light on the complex physics in this material, where strong electron-electron interaction interplays with a large spin-orbit coupling. - -This research work not only enhances our comprehension of the low-energy physics of Ba2IrO4 but paves also the way to study other spin-orbit materials with intriguing physics, especially the iridium-based compound Sr2IrO4. - -[1] V. I. Anisimov et al 1997 J. Phys.: Condens. Matter 9 7359 -[2] A. I. Lichtenstein and M. I. Katsnelson 1998 Phys. Rev. B 57 6884. -[3] S. Moser et al 2014 New J. Phys. 16 013008 -[4] J. Hubbard. 1963 Proc. R. Soc. London A 276 238 -[5] J. Kanamori 1963 Prog. Theor. Phys. 30 275–289 -[6] N. Marzari et al Rev. Mod. 2012 Phys. 84, 1419 -[7] F. Aryasetiawan et al 2004 Phys.Rev. B 70, 195104. -[8] P. Seth 2016 Comp. Phys. Com. 200 274-284 - -### Cesar Feniou (QUBITS-P, Paris) - -**Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer** - -Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) already hold the potential to outperform classical computing for simulating quantum many-body systems. However, their practical implementation on current quantum processing units (QPUs) is very challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and optimisation of a high-dimensional cost function. To overcome this, we propose new techniques to execute adaptive algorithms on a 25-qubit error-mitigated QPU coupled to a GPU-accelerated HPC simulator. Targeting physics applications, we compute the ground state of a 25-body Ising model using the newly introduced Greedy Gradient-free Adaptive VQE (CGA-VQE) requiring only five circuit measurements per iteration, regardless of the number of qubits and size of the operator pool. We show that the QPU successfully executes the algorithms and yields the correct choice of parametrised unitary operators. While the QPU evaluation of the resulting ansatz wave-function is polluted by hardware noise, a single final evaluation of the sought-after observables on a classical GPU-accelerated/noiseless simulator allows the recovery of the correct approximation of the ground state, thus highlighting the need for hybrid quantum-classical observable measurement. - ### Nicolas Laflorencie (LPT, Toulouse) **Topological and quantum critical properties of the interacting Majorana chain model** Despite our very good understanding of several models in one dimension involving interacting (Dirac) fermions, the case of Majorana fermions has remained relatively unexplored. This is probably due to the fact that Majorana particles are not found as elementary objects in nature. Nevertheless, 20 years ago, in the context of modeling p-wave superconducting wires, Alexei Kitaev proposed a very influential yet simple toy model in which unpaired Majorana fermions can appear as edge states. In this talk I will present the basics of this problem and explore the non-trivial effects of interactions in such a system, building on DMRG and self-consistent mean-field approaches. If time permits, I may also touch on disorder effects... -### Jack Thomas (LMO, Orsay) - -**Friedel oscillations in the reduced Hartree-Fock model** - -When a defect potential is placed in a material, the material rearranges and the total potential at long-range is screened by the electrons. In the finite temperature reduced Hartree-Fock model, small defects are completely screened [1]; the total change in potential decays exponentially. On the other hand, in metals at zero temperature, the presence of the Fermi-surface introduces non-analytic behaviour into the independent-particle susceptibility, leading to what are known as Friedel oscillations; the total potential oscillates and decays algebraically. In this talk, we will show how this rate of decay depends on the properties of the Fermi-surface. Joint work with Antoine Levitt. - -[1] Antoine Levitt, Archive for Rational Mechanics and Analysis 238 (2020) 901–927 - ### Pieter Van Isacker (GANIL, Caen) **Symmetries of nuclear models** @@ -167,24 +134,13 @@ The second approach, called ensemble-DFT, allows the direct extraction of quanti [9] F. Cernatic, B. Senjean, et al. Top. Curr. Chem. (Z) 380, 4 (2022) [10] F. Cernatic, P-F. Loos, B. Senjean, and E. Fromager, in preparation. -### Quentin Marecat (ICGM, Montpellier) - -**Recursive relations and quantum eigensolver algorithms within modified Schrieffer-Wolff transformations for the Hubbard dimer** - -The emergence of quantum computers has rekindled interest in solving the Hubbard model accurately for any dimension, size, regime, and filling. Several quantum algorithms have been proposed for this purpose, targeting both Noisy Intermediate Scale Quantum (NISQ) devices and long-term fault-tolerant quantum devices. These algorithms often employ hybrid classical/quantum strategies, such as the Variational Quantum Eigensolver (VQE), to optimize variational parameters on classical computers while applying parameterized unitary transformations on quantum devices. -One promising approach is the unitary Van-Vleck (VV) similarity transformation[1]. It involves designing a unitary transformation that rotates the Hubbard Hamiltonian into an effective Hamiltonian in the low-energy subspace. This transformation can be used to obtain the ground state (or excited states) of the Hubbard model on a quantum computer. However, finding an explicit expression for the VV generator is often challenging, necessitating truncation or approximations such as the Schrieffer and Wolff (SW) transformation[2]. -In this talk, I introduce modifications of the SW generator for the Hubbard dimer, providing both variational and iterative approaches. These modified SW transformations approximate, or even per- form the desired block-diagonalization of the Hubbard dimer at infinite perturbation order, similar to the VV generator. Two quantum algorithms associated with these modified SW transformations for the Hubbard dimer are presented, demonstrating their effectiveness, especially in the strongly interacting regime[3]. +### Diata Traore (QUBIT-P, Paris) -[1] I. Shavitt, and L. T. Redmon, "Quasidegenerate perturbation theories. A canonical van Vleck formalism and its relationship to other approaches.", The Journal of Chemical Physics 73, 5711- 5717. (1980). -[2] J.R. Schrieffer, and P.A. Wolff, "Relation between the Anderson and kondo hamiltonians", Physical Review 149, 491 (1966). -[3] Q. Marécat, B. Senjean and M. Saubanère, "Recursive relations and quantum eigensolver algorithms within modified Schrieffer- Wolff transformations for the Hubbard dimer.", Physical Review -B 107, 155110 (2023). +**TBA** -### Long Meng (CERMICS, Paris) +### Pina Romaniello (LPT, Toulouse) -**A Rigorous Justification Of Mittleman’s Approach To The Dirac–Fock Model** - -In this talk, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant $\alpha$ is small and the velocity of light $c$ is large. As a byproduct, we also prove, when $\alpha$ is small or $c$ is large, the no-unfilled shells theory in the Dirac–Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac-Fock model. +**TBA** ### David Gontier (CEREMADE, Paris) @@ -192,6 +148,20 @@ In this talk, we study the relationship between the Dirac–Fock model and the e The Peierls/SSH model is a simple one-dimensional model used to describe molecular chains such as polyacetylene. In this model, we consider a distortion energy between the atoms, and an electronic quantum energy given by a tight-binding model. Peierls showed that it was energetically favorable for the chain to dimerize (hence the structure …=C-C=C-… of polyacetylene). In this talk, we will study the phase diagram of this model, when we add temperature. We show the existence of a critical temperature above which the chain no longer dimerizes. Work in collaboration with Adéchola Kouandé and Éric Séré. +### Mauricio Rodríguez-Mayorga (Neel Institute, Grenoble) + +**Relativistic effects on the two-electron Harmonium atom** + +The non-relativistic Harmonium atom is a model system where parabolic confinement ($1⁄2\omega^2 r^2$) replaces the Coulombic ($-Z/r$) electron-nucleus interaction [1-4]. Varying the confinement strength (ω) enhances the different types of electronic correlation effects. Large (small) ω values make the weak (strong) electronic correlation dominant [1,3]. Consequently, this model system has served as a tool in the development and benchmarking of methods [5,6]. Moreover, analytic solutions for the two-electron Harmonium atom can also be obtained for certain ω values [4], which provides us with wavefunctions for two electrons that are explored to better understand the repercussions of electronic correlation effects. +In this work, we explore numerically the role of relativistic effects on the two-electron Harmonium. Our results indicate that only for the large $\omega$ values scalar relativistic effects are important and lead to a reduction of the total energy accompanied by changes in the electronic structure (e.g. a shrinking of the radial electronic density P(r)). + +[1] Cioslowski, J., & Pernal, K. (2000). The ground state of harmonium. J. Chem. Phys., 113, 8434-8443. +[2] Cioslowski, J. (2018). One-Electron Densities of Harmonium Atoms. In Theoretical and Quantum Chemistry at the Dawn of the 21st Century (pp. 349-380). Apple Academic Press. +[3] Cioslowski, J. (2018). Natural orbitals of the ground state of the two-electron harmonium atom. Theo. Chem. Acc, 137, 173. +[4] Taut, M. (1993). Two electrons in an external oscillator potential: Particular analytic solutions of a Coulomb correlation problem. Phys. Rev. A, 48, 3561. +[5] Rodríguez-Mayorga, M., Ramos-Cordoba, E., Via-Nadal, M., Piris, M., & Matito, E. (2017). Comprehensive benchmarking of density matrix functional approximations. Phys. Chem. Chem. Phys., 19, 24029. +[6] Jana, S., Behera, S. K., Śmiga, S., Constantin, L. A., & Samal, P. (2021). Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids. New J. Phys., 23, 063007. + # POSTERS ### Vitaly Gorelov (LSI, Palaiseau) @@ -202,10 +172,6 @@ The Peierls/SSH model is a simple one-dimensional model used to describe molecul **Emulation for (very) large scale PGCM computations of nuclei** -### Diata Traore (QUBIT-P, Paris) - -**TBA** - ### Jeremy Morere (LPCT, Nancy) **TBA** @@ -216,19 +182,55 @@ If we had access to the exact eigenstates of the stationary Hamiltonian, we coul As TD-DFT method do not allow the formulation of such operator, writing an approximate expression for these objects involves the use of a substitution operator. This operator is inspired by the operator that generates the central equation of the "Random Phase Approximation" method. We intend to demonstrate and justify why the choice of the complexity degree of the superoperators that can be involved in writing the expression of the two density matrices is not arbitrary. -### Mauricio Rodríguez-Mayorga (Neel Institute, Grenoble) +### Leo Gaspard (LCPQ, Toulouse) -**Relativistic effects on the two-electron Harmonium atom** +**Application of DMFT to realistic materials : the example of Ba2IrO4** -The non-relativistic Harmonium atom is a model system where parabolic confinement ($1⁄2\omega^2 r^2$) replaces the Coulombic ($-Z/r$) electron-nucleus interaction [1-4]. Varying the confinement strength (ω) enhances the different types of electronic correlation effects. Large (small) ω values make the weak (strong) electronic correlation dominant [1,3]. Consequently, this model system has served as a tool in the development and benchmarking of methods [5,6]. Moreover, analytic solutions for the two-electron Harmonium atom can also be obtained for certain ω values [4], which provides us with wavefunctions for two electrons that are explored to better understand the repercussions of electronic correlation effects. -In this work, we explore numerically the role of relativistic effects on the two-electron Harmonium. Our results indicate that only for the large $\omega$ values scalar relativistic effects are important and lead to a reduction of the total energy accompanied by changes in the electronic structure (e.g. a shrinking of the radial electronic density P(r)). +Describing the behavior of strongly correlated materials from first principles remains nowadays a challenge in computational condensed matter physics. Indeed, when Coulomb interaction is of the same order of magnitude as the kinetic energy of the electrons, like in materials with open d-shells, the Kohn-Sham band structure obtained within Density Functional Theory (DFT) is often quantitatively -- and even sometimes qualitatively -- wrong. To take strong correlations into account, Dynamical Mean Field Theory (DMFT) has been successfully coupled with DFT, in a scheme dubbed DFT+DMFT, to treat such systems for the past 25 years [1,2]. -[1] Cioslowski, J., & Pernal, K. (2000). The ground state of harmonium. J. Chem. Phys., 113, 8434-8443. -[2] Cioslowski, J. (2018). One-Electron Densities of Harmonium Atoms. In Theoretical and Quantum Chemistry at the Dawn of the 21st Century (pp. 349-380). Apple Academic Press. -[3] Cioslowski, J. (2018). Natural orbitals of the ground state of the two-electron harmonium atom. Theo. Chem. Acc, 137, 173. -[4] Taut, M. (1993). Two electrons in an external oscillator potential: Particular analytic solutions of a Coulomb correlation problem. Phys. Rev. A, 48, 3561. -[5] Rodríguez-Mayorga, M., Ramos-Cordoba, E., Via-Nadal, M., Piris, M., & Matito, E. (2017). Comprehensive benchmarking of density matrix functional approximations. Phys. Chem. Chem. Phys., 19, 24029. -[6] Jana, S., Behera, S. K., Śmiga, S., Constantin, L. A., & Samal, P. (2021). Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids. New J. Phys., 23, 063007. +In this talk, I will introduce how the state-of-the-art DFT+DMFT calculations can be performed, using the example of Ba2IrO4, a compound isostructural to the well-known La2CuO4 [3]: starting from a DFT calculation, a Hubbard-Kanamori-like model Hamiltonian is parametrized [4,5] using Wannier functions [6] and constrained Random Phase Approximation (cRPA) [7]. The model is then solved within DMFT using a continuous time Monte-Carlo solver in the Hybridization expansion (CT-HYB) scheme [8]. The calculated spectral function compares very well with available experimental angle-resolved photo-emission spectroscopy (ARPES) data [3] and sheds light on the complex physics in this material, where strong electron-electron interaction interplays with a large spin-orbit coupling. + +This research work not only enhances our comprehension of the low-energy physics of Ba2IrO4 but paves also the way to study other spin-orbit materials with intriguing physics, especially the iridium-based compound Sr2IrO4. + +[1] V. I. Anisimov et al 1997 J. Phys.: Condens. Matter 9 7359 +[2] A. I. Lichtenstein and M. I. Katsnelson 1998 Phys. Rev. B 57 6884. +[3] S. Moser et al 2014 New J. Phys. 16 013008 +[4] J. Hubbard. 1963 Proc. R. Soc. London A 276 238 +[5] J. Kanamori 1963 Prog. Theor. Phys. 30 275–289 +[6] N. Marzari et al Rev. Mod. 2012 Phys. 84, 1419 +[7] F. Aryasetiawan et al 2004 Phys.Rev. B 70, 195104. +[8] P. Seth 2016 Comp. Phys. Com. 200 274-284 +### Cesar Feniou (QUBITS-P, Paris) + +**Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer** + +Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) already hold the potential to outperform classical computing for simulating quantum many-body systems. However, their practical implementation on current quantum processing units (QPUs) is very challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and optimisation of a high-dimensional cost function. To overcome this, we propose new techniques to execute adaptive algorithms on a 25-qubit error-mitigated QPU coupled to a GPU-accelerated HPC simulator. Targeting physics applications, we compute the ground state of a 25-body Ising model using the newly introduced Greedy Gradient-free Adaptive VQE (CGA-VQE) requiring only five circuit measurements per iteration, regardless of the number of qubits and size of the operator pool. We show that the QPU successfully executes the algorithms and yields the correct choice of parametrised unitary operators. While the QPU evaluation of the resulting ansatz wave-function is polluted by hardware noise, a single final evaluation of the sought-after observables on a classical GPU-accelerated/noiseless simulator allows the recovery of the correct approximation of the ground state, thus highlighting the need for hybrid quantum-classical observable measurement. + +### Jack Thomas (LMO, Orsay) + +**Friedel oscillations in the reduced Hartree-Fock model** + +When a defect potential is placed in a material, the material rearranges and the total potential at long-range is screened by the electrons. In the finite temperature reduced Hartree-Fock model, small defects are completely screened [1]; the total change in potential decays exponentially. On the other hand, in metals at zero temperature, the presence of the Fermi-surface introduces non-analytic behaviour into the independent-particle susceptibility, leading to what are known as Friedel oscillations; the total potential oscillates and decays algebraically. In this talk, we will show how this rate of decay depends on the properties of the Fermi-surface. Joint work with Antoine Levitt. + +[1] Antoine Levitt, Archive for Rational Mechanics and Analysis 238 (2020) 901–927 + +### Quentin Marecat (ICGM, Montpellier) + +**Recursive relations and quantum eigensolver algorithms within modified Schrieffer-Wolff transformations for the Hubbard dimer** + +The emergence of quantum computers has rekindled interest in solving the Hubbard model accurately for any dimension, size, regime, and filling. Several quantum algorithms have been proposed for this purpose, targeting both Noisy Intermediate Scale Quantum (NISQ) devices and long-term fault-tolerant quantum devices. These algorithms often employ hybrid classical/quantum strategies, such as the Variational Quantum Eigensolver (VQE), to optimize variational parameters on classical computers while applying parameterized unitary transformations on quantum devices. +One promising approach is the unitary Van-Vleck (VV) similarity transformation[1]. It involves designing a unitary transformation that rotates the Hubbard Hamiltonian into an effective Hamiltonian in the low-energy subspace. This transformation can be used to obtain the ground state (or excited states) of the Hubbard model on a quantum computer. However, finding an explicit expression for the VV generator is often challenging, necessitating truncation or approximations such as the Schrieffer and Wolff (SW) transformation[2]. +In this talk, I introduce modifications of the SW generator for the Hubbard dimer, providing both variational and iterative approaches. These modified SW transformations approximate, or even per- form the desired block-diagonalization of the Hubbard dimer at infinite perturbation order, similar to the VV generator. Two quantum algorithms associated with these modified SW transformations for the Hubbard dimer are presented, demonstrating their effectiveness, especially in the strongly interacting regime[3]. + +[1] I. Shavitt, and L. T. Redmon, "Quasidegenerate perturbation theories. A canonical van Vleck formalism and its relationship to other approaches.", The Journal of Chemical Physics 73, 5711- 5717. (1980). +[2] J.R. Schrieffer, and P.A. Wolff, "Relation between the Anderson and kondo hamiltonians", Physical Review 149, 491 (1966). +[3] Q. Marécat, B. Senjean and M. Saubanère, "Recursive relations and quantum eigensolver algorithms within modified Schrieffer- Wolff transformations for the Hubbard dimer.", Physical Review +B 107, 155110 (2023). + +### Long Meng (CERMICS, Paris) + +**A Rigorous Justification Of Mittleman’s Approach To The Dirac–Fock Model** + +In this talk, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant $\alpha$ is small and the velocity of light $c$ is large. As a byproduct, we also prove, when $\alpha$ is small or $c$ is large, the no-unfilled shells theory in the Dirac–Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac-Fock model. -