A mean-field approach to attractive few-body Fermi gas
Abstract: Quantum many-body systems can be studied theoretically from first principles using microscopic models, but the computational cost of numerically exact calculations increases exponentially with the number of particles and the complexity of the interaction, limiting the systems that can be analysed. The Hartree-Fock-Bogoliubov (HFB) and quasiparticle random phase approximation (QRPA) methods, heavily used in nuclear physics, rely on mean-field approximations but scale more favourably with increasing system size and complexity. In this work we apply these methods to the problem of a two-dimensional harmonically trapped Fermi gas with attractive interactions, with the goal of investigating the validity of the approximations in the few-body limit. We implement the approximate methods in code and then compare them with exact calculations. We find that the HFB method can account for pairing correlations that arise due to the attractive interaction, predicting well the ground state energy even at high interaction strengths. Also, the excitation spectra predicted by the QRPA method qualitatively match the true spectra, reproducing the expected subset of excitations. Finally, we see that perturbative corrections can be used to improve the ground state energy estimate of the HFB.
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