A Manybody Formalism for Fermions, Enforcing the Pauli Principle on Paper

TL;DR

This paper introduces a scalable many-body formalism for fermions that enforces the Pauli principle analytically, enabling efficient study of large fermionic systems like the unitary Fermi gas.

Contribution

The paper extends a symmetry invariant perturbation theory to fermions, allowing analytical treatment of large systems without complex numerical enforcement of the Pauli principle.

Findings

Method accurately models a unitary Fermi gas

Minimal computational cost for large systems

Results agree with Monte Carlo simulations

Abstract

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 manybody 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 which 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.