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Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order M{\o}ller-Plesset partitioning of the Hamiltonian is used to obtain the well known…
Present atomic theory provides accurate and reliable results for atoms with a small number of valence electrons. However, most current methods of calculations fail when the number of valence electrons exceeds four or five. This means that…
We propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments, and…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition…
We present new formulae for the matrix elements of one-body and two-body physical operators in compact forms, which are applicable to arbitrary Hartree-Fock-Bogoliubov wave functions, including those for multi-quasiparticle excitations. The…
Second-order Moller-Plesset perturbation theory (MP2) for ab initio simulations of solids is often limited by divergence or over-correlation issues, particularly in metallic, narrow-gap, and dispersion-stabilized systems. We develop and…
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
Perturbative methods are attractive to describe the electronic structure of molecular systems because of their low-computational cost and systematically improvable character. In this work, a two-step perturbative approach is introduced…
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent…
To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…
This article is an introduction to a new approach to first principles electronic structure calculation. The starting point is the Hartree-Fock-Roothaan equation, in which molecular integrals are approximated by polynomials by way of Taylor…
We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order [T.…
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
A formalism for energy-dependent many-body perturbation theory (MBPT), previously indicated in our recent review articles (Lindgren et al., Phys.Rep. 389,161(2004), Can.J.Phys. 83,183(2005)), is developed in more detail. The formalism…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…