The name is absent

16

∑_k(2¾Γ¹ with 6_k = ħ~k²1(2m). Note that we have ignored the Hartree shift in the BdG
equation. In the mean-field level, it is reasonable to thedrop the Hartree term at unitarity
limit [22].

3.2 Self-consistent numerical solutions of the BDG equa-
tion

Our aim is to search for the ground state by solving the BdG equation above self-consistently.
Such self-consistent calculation requires huge computational resources and time, therefore
an effective numerical scheme and parallelization of the program will be necessary. We
adopt a hybrid strategy as detailed in Ref. [22], where it has been used to successfully
solve BdG equation in an effective ID case. In short, the basic idea for this strategy is
that a cutoff energy E_c is introduced. Quasiparticle modes with ∣E₇I < E_c are calculated
by solving Eqs. (3.2); while the high-energy modes with ∣E₇∙∣ > E_c are calculated using
the semi-classical method in the spirit of the LDA. In our practice, we have found this
technique to be very efficient in the sense that it does not require a very large E_c (typical
values of E_c we used is a few times Fermi energy) and the results are essentially cutoff-
independent. For each run, we choose T, a_s and λ. We then either fix the values for N_σ, or
that for μ_σ, which is referred as canonical or grand-canonical mode respectively and solve
Eqs. (3.2) Self-Consistently together with the above-cutoff modes.

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