Hartree-Fock and Random Phase Approximation theories in a many-fermion solvable model

TL;DR

This paper introduces an exactly solvable many-fermion model to evaluate the accuracy of Hartree-Fock and Random Phase Approximation methods, showing their improving performance with larger particle numbers.

Contribution

It provides an ideal test system for benchmarking and analyzing the validity of common many-body approximation techniques.

Findings

Hartree-Fock accuracy improves with more particles

RPA provides reliable excitation descriptions in the model

Exact solutions serve as benchmarks for approximate methods

Abstract

We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree-Fock and the Random Phase Approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.