Related papers: Tensor factorizations of local second-order M{\o}l…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…
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…
The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…
We compute the orbital magnetization in real materials by evaluating a recently discovered formula for periodic systems, within density functional theory. We obtain improved values of the orbital magnetization in the ferromagnetic metals…
Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron…
We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models…
We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three dimensional periodic systems in second-order M{\o}ller-Plesset perturbation theory (MP2). In particular we…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…
A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for…
A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed and demonstrated using full configuration interaction (FCI) simulations and…
We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This…
Maximally localized Wannier functions are widely used in electronic structure theory for analyses of bonding, electric polarization, orbital magnetization, and for interpolation. The state of the art method for their construction is based…
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on…
We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz…