Related papers: Angular reduction in multiparticle matrix elements
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…
The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to…
The angular spectrum of a vectorial laser beam is expressed in terms of an intrinsic coordinate system instead of the usual Cartesian laboratory coordinates. This switch leads to simple, elegant and new expressions such as for the angular…
Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators…
Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both…
Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often…
The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…
We show that tensor products of $k$ gradients of harmonic functions, with $k$ at least three, are dense in $C(\overline{\Omega})$, for any bounded domain $\Omega$ in dimension 3 or higher. The bulk of the argument consists in showing that…
An original presentation of Categorical Quantum Physics, in the line of Abramsky and Coecke, tries to introduce only objects and assumptions that are clearly relevant to Physics and does not assume compact closure. Adjoint arrows, tensor…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
We discuss a new method of integration over matrix variables based on a suitable gauge choice in which the angular variables decouple from the eigenvalues at least for a class of two-matrix models. The calculation of correlation functions…
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how…
We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…