Antoine Levitt

Bio: Antoine Levitt is an academic researcher from University of Paris. The author has contributed to research in topics: Physics & Wannier function. The author has an hindex of 9, co-authored 39 publications receiving 801 citations. Previous affiliations of Antoine Levitt include École Normale Supérieure & CEREMADE.

Robust determination of maximally localized Wannier functions

Abstract: We propose an algorithm to determine maximally localized Wannier functions (MLWFs). This algorithm, based on recent theoretical developments, does not require any physical input such as initial guesses for the Wannier functions, unlike popular schemes based on the projection method. We discuss how the projection method can fail on fine grids when the initial guesses are too far from MLWFs. We demonstrate that our algorithm is able to find localized Wannier functions through tests on two-dimensional systems, simplified models of semiconductors, and realistic DFT systems by interfacing with the wannier90 code. We also test our algorithm on the Haldane and Kane-Mele models to examine how it fails in the presence of topological obstructions.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

Abstract: We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top ...

Convergence of gradient-based algorithms for the Hartree-Fock equations∗

Abstract: The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cances and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient inequality for analytic functionals due to Łojasiewicz [Ensembles semi-analytiques . Institut des Hautes Etudes Scientifiques (1965)]. Then, expanding upon the analysis of [E. Cances and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], we prove convergence results for the Roothaan and Level-Shifting algorithms. In each case, our method of proof provides estimates on the convergence rate. We compare these with numerical results for the algorithms studied.

Bose-Einstein condensation in a gas of sodium atoms

Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Methods Of Modern Mathematical Physics

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PySCF: the Python-based simulations of chemistry framework

Abstract: Python-based simulations of chemistry framework (PySCF) is a general-purpose electronic structure platform designed from the ground up to emphasize code simplicity, so as to facilitate new method development and enable flexible computational workflows. The package provides a wide range of tools to support simulations of finite-size systems, extended systems with periodic boundary conditions, low-dimensional periodic systems, and custom Hamiltonians, using mean-field and post-mean-field methods with standard Gaussian basis functions. To ensure ease of extensibility, PySCF uses the Python language to implement almost all of its features, while computationally critical paths are implemented with heavily optimized C routines. Using this combined Python/C implementation, the package is as efficient as the best existing C or Fortran-based quantum chemistry programs. In this paper, we document the capabilities and design philosophy of the current version of the PySCF package. WIREs Comput Mol Sci 2018, 8:e1340. doi: 10.1002/wcms.1340 This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry