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Abstract

We consider the problem of extrapolating the perturbation series for the
dilute Fermi gas in three dimensions to the unitary limit of infinite
scattering length and into the BEC region, using the available strong-coupling
information to constrain the extrapolation problem. In this constrained
extrapolation problem (CEP) the goal is to find classes of approximants that
give well converged results already for low perturbative truncation orders.
First, we show that standard Padé and Borel methods are too restrictive to
give satisfactory results for this CEP. A generalization of Borel extrapolation
is given by the so-called Maximum Entropy extrapolation method (MaxEnt).
However, we show that MaxEnt requires extensive elaborations to be applicable
to the dilute Fermi gas and is thus not practical for the CEP in this case.
Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple,
practical, and general method for the CEP. We find that the ODME approximants
for the ground-state energy of the dilute Fermi gas are robust with respect to
changes of the mapping choice and agree with results from quantum Monte Carlo
simulations within uncertainties.