Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation

Since the ’30s the interatomic potential of the beryllium dimer Be_22 has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be_22 along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be_22 interatomic potential using the GWGW approximation and the Bethe-Salpeter equation (BSE). The ground-state correlation energy is calculated by the trace formula with checks against the adiabatic-connection fluctuation-dissipation theorem formula. We show that inclusion of GWGW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GWGW approximation, our calculation is in surprising agreement with the most accurate theories and with experiment. It even reproduces an experimentally observed flattening of the interatomic potential due to a delicate correlations balance from a competition between covalent and van der Waals bonding.

The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential V(x)V(x). Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables \hat{O} (x)Ô(x) in the microscopic model with their field theory counterparts \partial_x h, e^{i h(x)}, e^{-i h(x)}∂xh,eih(x),e−ih(x), etc., which involve non-universal coefficients that themselves depend on position — a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids —, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

AN ATTEMPT AT A RESONATING MEAN-FIELD THEORETICAL DESCRIPTION OF THERMAL BEHAVIOR OF TWO-GAP SUPERCONDUCTIVITY

The resonating mean-field theory (Res-MFT) has been applied and shown to effectively describe two-gap superconductivity (SC). Particularly at T = 0 using a suitable chemical potential, the two-gap SC in MgB2 has been well described by the Res-Hartree-Bogoliubov theory (Res-HBT). The Res-HB ground state generated with HB wavefunctions almost exhausts the ground-state correlation energy in all the correlation regimes. In this paper we make an attempt at a Res-MF theoretical description of thermal behavior of the two-gap SC. In an equal energy-gap case we find a new formula leading to a higher critical temperature Tc than the Tc of the usual HB formula.