Numerical Exact Solutions to the Many-body Problem Based on the Differential Forms

Abstract

The Many-body problem is very important issue in physics. Usually perturbation calculations based on the Green's function have been used to analyze such a problem, however, infinite orders of perturbation calculations are required to obtain exact solutions, thus resulting in the analytical and numerical difficulties. To overhaul such difficulties, we propose the new calculation method based on the differential forms, which are able to evaluate exact solutions if Hamiltonian is composed of Fermi particles. Since our proposed method is based on time evolution equations, comparisons with the calculations derived from Feynman Kernel is possible, with showing complete agreement. Furthermore we applied this method to the simplest Anderson Hamiltonian to investigate the appearance of magnetic moment. The calculation results show that magnetic moment easily disappears with small Coulomb repulsive energy, possibly implying the spin fluctuations.