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arXiv:physics/0603093 · Physical Review B

Regime of validity of the pairing Hamiltonian in the study of Fermi gases

S. Y. Chang, Vijay R. Pandharipande

Published Jun 6, 2006• 0 citations
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Abstract

The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting $(1∕a{k}_{F}⪡0)$ regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, $1∕a{k}_{F}\ensuremath{\gtrsim}0$, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength $\ensuremath{-}\ensuremath{\infty}<1∕a{k}_{F}<0$ such as $a{k}_{F}\ensuremath{\sim}\ensuremath{-}1$.

DOI
10.1103/physrevb.73.212502

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The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting (1∕akF⪡0)(1∕a{k}_{F}⪡0)(1∕akF​⪡0) regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, 1∕akF\ensuremath≳01∕a{k}_{F}\ensuremath{\gtrsim}01∕akF​\ensuremath≳0, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength \ensuremath−\ensuremath∞<1∕akF<0\ensuremath{-}\ensuremath{\infty}<1∕a{k}_{F}<0\ensuremath−\ensuremath∞<1∕akF​<0 such as akF\ensuremath∼\ensuremath−1a{k}_{F}\ensuremath{\sim}\ensuremath{-}1akF​\ensuremath∼\ensuremath−1.
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The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.
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