1,085 research outputs found
Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally
expensive part in self-consistent density functional theory (DFT) calculations.
In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace
iteration method, which avoids computing explicit eigenvectors except at the
first SCF iteration. The method may be viewed as an approach to solve the
original nonlinear Kohn-Sham equation by a nonlinear subspace iteration
technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue
problem. It reaches self-consistency within a similar number of SCF iterations
as eigensolver-based approaches. However, replacing the standard
diagonalization at each SCF iteration by a Chebyshev subspace filtering step
results in a significant speedup over methods based on standard
diagonalization. Here, we discuss an approach for implementing this method in
multi-processor, parallel environment. Numerical results are presented to show
that the method enables to perform a class of highly challenging DFT
calculations that were not feasible before
Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
We implemented the charge self-consistent combination of Density Functional
Theory and Dynamical Mean Field Theory (DMFT) in two full-potential methods,
the Augmented Plane Wave and the Linear Muffin-Tin Orbital methods. We
categorize the commonly used projection methods in terms of the causality of
the resulting DMFT equations and the amount of partial spectral weight
retained. The detailed flow of the Dynamical Mean Field algorithm is described,
including the computation of response functions such as transport coefficients.
We discuss the implementation of the impurity solvers based on hybridization
expansion and an analytic continuation method for self-energy. We also derive
the formalism for the bold continuous time quantum Monte Carlo method. We test
our method on a classic problem in strongly correlated physics, the
isostructural transition in Ce metal. We apply our method to the class of heavy
fermion materials CeIrIn_5, CeCoIn_5 and CeRhIn_5 and show that the Ce 4f
electrons are more localized in CeRhIn_5 than in the other two, a result
corroborated by experiment. We show that CeIrIn_5 is the most itinerant and has
a very anisotropic hybridization, pointing mostly towards the out-of-plane In
atoms. In CeRhIn_5 we stabilized the antiferromagnetic DMFT solution below 3K,
in close agreement with the experimental N\'eel temperature.Comment: The implementation of Bold-CTQMC added and some test of the method
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Decay properties of spectral projectors with applications to electronic structure
Motivated by applications in quantum chemistry and solid state physics, we
apply general results from approximation theory and matrix analysis to the
study of the decay properties of spectral projectors associated with large and
sparse Hermitian matrices. Our theory leads to a rigorous proof of the
exponential off-diagonal decay ("nearsightedness") for the density matrix of
gapped systems at zero electronic temperature in both orthogonal and
non-orthogonal representations, thus providing a firm theoretical basis for the
possibility of linear scaling methods in electronic structure calculations for
non-metallic systems. We further discuss the case of density matrices for
metallic systems at positive electronic temperature. A few other possible
applications are also discussed.Comment: 63 pages, 13 figure
One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
In this review we provide a rigorous and self-contained presentation of
one-body reduced density-matrix (1RDM) functional theory. We do so for the case
of a finite basis set, where density-functional theory (DFT) implicitly becomes
a 1RDM functional theory. To avoid non-uniqueness issues we consider the case
of fermionic and bosonic systems at elevated temperature and variable particle
number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space
is finite-dimensional due to the Pauli principle and we can provide a rigorous
1RDM functional theory relatively straightforwardly. For the bosonic case,
where arbitrarily many particles can occupy a single state, the Fock space is
infinite-dimensional and mathematical subtleties (not every hermitian
Hamiltonian is self-adjoint, expectation values can become infinite, and not
every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose
restrictions on the allowed Hamiltonians and external non-local potentials. For
simple conditions on the interaction of the bosons a rigorous 1RDM functional
theory can be established, where we exploit the fact that due to the finite
one-particle space all 1RDMs are finite-dimensional. We also discuss the
problems arising from 1RDM functional theory as well as DFT formulated for an
infinite-dimensional one-particle space.Comment: 55 pages, 7 figure
New Algebraic Formulation of Density Functional Calculation
This article addresses a fundamental problem faced by the ab initio
community: the lack of an effective formalism for the rapid exploration and
exchange of new methods. To rectify this, we introduce a novel, basis-set
independent, matrix-based formulation of generalized density functional
theories which reduces the development, implementation, and dissemination of
new ab initio techniques to the derivation and transcription of a few lines of
algebra. This new framework enables us to concisely demystify the inner
workings of fully functional, highly efficient modern ab initio codes and to
give complete instructions for the construction of such for calculations
employing arbitrary basis sets. Within this framework, we also discuss in full
detail a variety of leading-edge ab initio techniques, minimization algorithms,
and highly efficient computational kernels for use with scalar as well as
shared and distributed-memory supercomputer architectures
Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
With the objective of employing graphs toward a more generalized theory of
signal processing, we present a novel sampling framework for (wavelet-)sparse
signals defined on circulant graphs which extends basic properties of Finite
Rate of Innovation (FRI) theory to the graph domain, and can be applied to
arbitrary graphs via suitable approximation schemes. At its core, the
introduced Graph-FRI-framework states that any K-sparse signal on the vertices
of a circulant graph can be perfectly reconstructed from its
dimensionality-reduced representation in the graph spectral domain, the Graph
Fourier Transform (GFT), of minimum size 2K. By leveraging the recently
developed theory of e-splines and e-spline wavelets on graphs, one can
decompose this graph spectral transformation into the multiresolution low-pass
filtering operation with a graph e-spline filter, and subsequent transformation
to the spectral graph domain; this allows to infer a distinct sampling pattern,
and, ultimately, the structure of an associated coarsened graph, which
preserves essential properties of the original, including circularity and,
where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017
Circulant Matrices and Their Application to Vibration Analysis
International audienceThis paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. Our presentation of the basic theory is distilled from the classic book of Davis (1979, Circulant Matrices, 2nd ed., Wiley, New York) with results, proofs, and examples geared specifically to vibration applications. Our aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications , and generalizations of the theory
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
From spline wavelet to sampling theory on circulant graphs and beyond– conceiving sparsity in graph signal processing
Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs.
Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations.
Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes.
Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.Open Acces
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