Related papers: Exact Two-body Expansion of the Many-particle Wave…
As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this work we explore the extension…
Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact 4-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The…
Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave…
A recent work [arXiv:2401.04685] has merged $N$-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the…
The direct solution of the many-particle Schr\"odinger equation is computationally inaccessible for more than very few electrons. In order to surpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007, 98 (066803)] has…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
This paper derives and demonstrates a new, purely density-based ab initio approach for calculation of the energies and properties of many-electron systems. It is based upon the discovery of relationships that govern the "mechanics" of the…
The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented…
Within the hyperspherical framework, the solution of the time-independent Schroedinger equation for a n-particle system is divided into two steps, the solution of a Schroedinger like equation in the hyperangular degrees of freedom and the…
We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body…
We present a formal derivation of the many-body perturbation theory for a system of electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is treated at an arbitrary high order of bosons scattered. The…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In this work, we use a newly discovered fourth order…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e.…
A simple explanation is given for the exactness of the extended Koopmans' theorem for computing the removal energy of any many-electron system to the lowest-energy ground state ion of a given symmetry. In particular, by removing the…
In this study, we utilize the many-body expansion (MBE) framework to decompose electronic structures into fragments by incrementing the virtual orbitals. Our work aims to accurately solve the ground and excited state energies of each…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…