Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGround-state correlation energy of beryllium dimer by the Bethe-Salpeter equation
94
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Since the 30s the interatomic potential of the beryllium dimer Be$_2$ has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be$_2$ along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be$_2$ interatomic potential using the GW 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 GW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GW 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.
rate research
Read More
We check the ab initio GW approximation and Bethe-Salpeter equation (BSE) many-body methodology against the exact solution benchmark of the hydrogen molecule H$_2$ ground state and excitation spectrum, and in comparison with the configuration interaction (CI) and time-dependent Hartree-Fock methods. The comparison is made on all the states we could unambiguously identify from the excitonic wave functions symmetry. At the equilibrium distance $R = 1.4 , a_0$, the GW+BSE energy levels are in good agreement with the exact results, with an accuracy of 0.1~0.2 eV. GW+BSE potential-energy curves are also in good agreement with the CI and the exact result up to $2.3 , a_0$. The solution no longer exists beyond $3.0 , a_0$ for triplets ($4.3 , a_0$ for singlets) due to instability of the ground state. We tried to improve the GW reference ground state by a renormalized random-phase approximation (r-RPA), but this did not solve the problem.
The problem of a relativistic bound-state system consisting of two scalar bosons interacting through the exchange of another scalar boson, in 2+1 space-time dimensions, has been studied. The Bethe-Salpeter equation (BSE) was solved by adopting the Nakanishi integral representation (NIR) and the Light-Front projection. The NIR allows us to solve the BSE in Minkowski space, which is a big and important challenge, since most of non-perturbative calculations are done in Euclidean space, e.g. Lattice and Schwinger-Dyson calculations. We have in this work adopted an interaction kernel containing the ladder and cross-ladder exchanges. In order to check that the NIR is also a good representation in 2+1, the coupling constants and Wick-rotated amplitudes have been computed and compared with calculations performed in Euclidean space. Very good agreement between the calculations performed in the Minkowski and Euclidean spaces has been found. This is an important consistence test that allows Minkowski calculations with the Nakanishi representation in 2+1 dimensions. This relativistic approach will allow us to perform applications in condensed matter problems in a near future.
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter amplitude itself. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange is computed for the first time.
The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.
The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
