Related papers: Fourth-order perturbative extension of the single-…
Atomic nuclei can exhibit shape coexistence and multi-reference physics that enters in their ground states, and to accurately capture the ensuing correlations and entanglement is challenging. We address this problem by applying…
Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…
Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to…
We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…
An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
We study the convergence of a linear atomic cluster expansion (ACE) potential with respect to its basis functions, in terms of the effective two-body interactions of elemental Carbon and Silicon systems. We build ACE potentials with…
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep…
We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construction of the $q$-difference Painlev\'e equations, showing…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are…
I present a derivation of form factors in the Algebraic Cluster Model for an arbitrary number of identical clusters. The form factors correspond to representation matrix elements which are derived in closed form for the harmonic oscillator…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the…
In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree…
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI)…
The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of…
Elastic-scattering phase shifts for four-nucleon systems are studied in an $ab$-$initio$ type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy $d+d$ and $t+p$ scattering. In…