Two-Body Orbitals for One-Dimensional Fermion Gas with Application to Repulsive δ-Function Interactions

Abstract

Explicit strongly orthogonal two-body orbitals (geminals) are constructed from free-particle Wannier functions for the lowest singlet state of a one-dimensional homogeneous fermion gas. As an application of the method, the ground-state energy is evaluated for repulsive delta function interactions for a range of the coupling constant. For weak coupling, the present method yields a lower energy than that of the Overhauser state. Using second-order perturbation corrections as a means of comparison, it is found that, in the high-density limit, the strongly orthogonal geminal product gives only a fifth of the total correlation energy. In the strong coupling regime, the results are more favorable but it proves difficult to determine the asymptotic behavior.