Related papers: Implicit Purification for Temperature-Dependent De…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
Purification is a tool that allows to represent mixed quantum states as pure states on enlarged Hilbert spaces. A purification of a given state is not unique and its entanglement strongly depends on the particular choice made. Moreover, in…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
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…
An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p.…
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…
It is by now well-known that ground states of gapped one-dimensional (1d) quantum-many body systems with short-range interactions can be studied efficiently using classical computers and matrix product state techniques. A corresponding…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures.…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free energy ensembles in tight-binding, Hartree-Fock or Kohn-Sham density functional theory. The canonical…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
The stress integration of critical soil model is usually based on implicit Euler algorithm, where the stress predictor is corrected by employing a return mapping algorithm. In the case of large load step, the solution of local nonlinear…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…