Related papers: Tensor factorizations of local second-order M{\o}l…

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…

Source localization and radio cartography using multi-way representation of spectrum is the subject of study in this paper. A joint matrix factorization and tensor decomposition problem is proposed and solved using an iterative algorithm.…

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in…

Whether for fundamental studies or nuclear data evaluations, first-principle calculations of atomic nuclei constitute the path forward. Today, performing \textit{ab initio} calculations (a) of heavy nuclei, (b) of doubly open-shell nuclei…

We present the Electronic Tensor Reconstruction Algorithm (ELECTRA) - an equivariant model for predicting electronic charge densities using floating orbitals. Floating orbitals are a long-standing concept in the quantum chemistry community…

A new method is presented that allows for efficient evaluation of spin-orbit coupling (SOC) in density-functional theory calculations. In the so-called second-variational scheme, where Kohn-Sham functions obtained in a scalar-relativistic…

Construction of hybrid atomic orbitals is proposed as the approximate common eigen states of finite first moment matrices. Their hybridization and orientation can be a-priori tunned as per their anticipated neighbourhood. Their Wannier…

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…

The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions…

We provide an efficient approximation for the exponential of a local operator in quantum spin systems using tensor-network representations of a cluster expansion. We benchmark this cluster tensor network operator (cluster TNO) for…

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…

We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine-learning energy models of solids and molecules. This allows us to describe, on the same…

The simultaneous treatment of static and dynamical correlations in strongly-correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the…

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

Occupation numbers of natural orbitals capture the physics of strong electron correlations in momentum space. A Natural Orbital Density Functional Theory based on the antisymmetrized geminal product provides these occupation numbers and the…

Two-dimensional materials are a highly tunable platform for studying the momentum space topology of the electronic wavefunctions and real space topology in terms of skyrmions, merons, and vortices of an order parameter. Such textures for…

As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…

Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the…