Extension of the Hartree method to strongly interacting systems

Masatoshi Yamamura, A. Kuriyama

日本物理学会, 京都大学基礎物理学研究所, 正俊 山村 +1 more

M. C. Cambiaggio, J. Dukelsky, Guillermo R. Zemba

An extension to bosons of a constrained Hartree variational method is developed in which an angular momentum constraint is imposed. The method is applied to a soluble bosonic model, the Q-consistent Hamiltonian of Warner and Casten (1982). The results are compared not only with the exact ones but also with those obtained from the cranked Hartree variational approximation.

Joshua Cesca, C. Simenel

Background: The Hartree-Fock mean-field approximation is standard in combination with energy density functionals (EDF) that account for some dynamical correlations. Breaking and restoring the symmetries of the system allow for the inclusion of additional static correlations. However, exact solutions to evaluate the effectiveness of these methods are rare.Purpose: To benchmark the Hartree-Fock method with broken and restored rotational symmetry in a system of identical interacting fermions on a one-dimensional quantum ring using model interactions.Method: The ground-state wave function is found using the Hartree-Fock method both with rotational invariance and with the symmetry broken at the mean-field level. Rotational symmetry is then restored with an angular momentum projection method. The ground-state energies are compared to variational Monte Carlo predictions. This is done for a range of different interactions between the particles.Results: Breaking the rotational symmetry in the Hartree-Fock mean-field brings little improvement to the ground-state energy in weakly repulsive systems or attractive systems confined on small rings. Larger improvements are found in strongly repulsive systems and attractive systems on larger rings in which the particles form a self-bound system. Symmetry restoration brought only small improvements in most cases but was able to account for most of the remaining correlation energy (after symmetry breaking) in repulsive systems.Conclusions: The effectiveness of incorporating correlations through rotational symmetry breaking followed by angular momentum projection is demonstrated for one-dimensional quantum rings using model interactions, encouraging generalisations to other symmetries, extensions to higher dimensions, as well as applications in the EDF framework.

Rishabh Jha

Richard J. Eden

The Hartree self-consistent method is generalized to apply to a system with strong two-body correlations. The generalized Hartree method is shown to be equivalent to solving a self-consistent equation for the mutual interaction of two particles moving in average fields together with a Hartree-Fock variational problem. In this form the method is equivalent to, and provides a simple explanation of, the nuclear saturation procedure used by Brueckner, Levinson, and Mahmoud.