Fermions on a Quantum Ring

Abstract

Model systems are an effective tool for testing approximate methods for solving the quantum many-body problem. This thesis used an idealised 1-D quantum ring of fermions to test rotational symmetry breaking and rotational symmetry restoration in the Hartree-Fock method when applied to Coulomb and nuclear-like systems. This was achieved by comparing the exact ground state energy, which was found using the variational Monte Carlo method, to the predicted ground state energies of the Hartree-Fock method without rotational symmetry breaking, with rotational symmetry breaking, and with rotational symmetry restored. It was found that the effectiveness of symmetry breaking in systems with repulsive interactions between particles increased with the strength of the interaction. In systems with attractive interactions, symmetry breaking significantly improved the Hartree-Fock energy but still failed to account for all of the correlation energy of the ground state. Symmetry restoration was able to account for almost all of the correlation energy in repulsive systems but typically gave little improvement to the symmetry-broken energy in attractive systems. Show more