Related papers: Ground state of Li and Be$^+$ using explicitly cor…
We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove convergence of the ground state energy to the minimizer of a…
The Hylleraas-B-splines basis set is introduced in this paper, which can be used to obtain the eigenvalues and eigenstates of helium-like system's Hamiltonian. Comparing with traditional B-splines basis, the rate of convergence of our…
The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H$_2^+$, D$_2^+$, and HD$^+$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly…
Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
The average ground state energy and entropy for +/- J spin glasses on Bethe lattices of connectivities k+1=3...,26 at T=0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n=2048), the Extremal…
The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that…
The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12…
In this work we propose a novel composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorisable coupled…
Using the exact Bethe Ansatz solution, we investigate methods for calculating the ground-state energy for the $p + ip$-pairing Hamiltonian. We first consider the Hamiltonian isolated from its environment (closed model) through two forms of…
We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the…
Calculations of the positron-Li system were performed using the Stochastic Variational Method and yielded a minimum energy of -7.53208 Hartree for the L=0 ground state. Unlike previous calculations of this system, the system was found to be…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…
We extract energies and widths of the ground states of $^5$He and $^5$Li from recent single--level R--matrix fits to the spectra of the $^3$H$({\rm d},\gamma$)$^5$He and the $^3$He$({\rm d},\gamma$)$^5$Li reactions. The widths obtained…
We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$\zeta$…
We predict ground-state energies of $^3$H, $^4$He, and $^6$Li in chiral effective field theory up to next-to-next-to-next-to-leading-order (N$^3$LO) using a power counting guided by renormalization-group invariance. Subleading two-nucleon…
In this work, we report an application of Hylleraas-$B$-spline basis set to the nonrelativistic Bethe logarithm calculation of helium. The Bethe logarithm for $n\ ^1S$, $n$ up to 10, states of helium are calculated with a precision of 7-9…
This paper investigates numerical methods for approximating the ground state of Bose--Einstein condensates (BECs) by introducing two relaxed formulations of the Gross--Pitaevskii energy functional. These formulations achieve first- and…
The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…