Ground State Properties with a Random Two-Body Interaction

We apply a two-body random ensemble to a hypothetical system of spinless fermionsoccupying a one-dimensional rotationally invariant orbit in order to study the statisticaltendencies of spins of ground states for a random two-body interaction. We also investigatethe origin of the dominance of spin-zero ground states of a single-jshell in the nuclear shellmodel, which can be interpreted geometrically as a particular case of the simple hypotheticalmodel we consider. Assuming a specific symmetry, or the doublet structure due to time-reversal symmetry, it is found that the ensemble has a preference for a ground state whosespin is zero. We demonstrate how the time-reversal symmetry and its doublet structureaffect this ground state tendency.status: publishe