Many-body formalism for fermions: Enforcing the Pauli principle on paper

Confined quantum systems involving $N$ identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with $N$ and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.

Figure 1

Energies of the harmonically trapped unitary Fermi gas (units $\hslash {\omega }_{ho}=1$). Our first-order perturbation results (filled diamonds) are compared to GFMC (+'s) [27], fixed-node DMC (open circles) from Ref. [8], and AFMC results (filled circles, $N$ = 6, 8, 14, 20, and 30 only) [28].

Figure 2

Energies of the harmonically trapped unitary Fermi gas (units $\hslash {\omega }_{ho}=1$). Our first-order perturbation results (filled diamonds) are compared to DMC results Ref. [28] (open squares).