Fermi Momentum and Friends

The square of the Fermi momentum is calculable without explicitly picking a scale, as long as we agree to multiply by the scattering length

Fermi Momentum

tdg.observable.fermi.kFa_squared(ensemble)

\((k_F a)^2 = N \tilde{a}^2 / 2\pi\).

tdg.observable.fermi.kFa(ensemble)

\(\sqrt{\texttt{kFa_squared}}\).

tdg.observable.fermi.log_kFa(ensemble)

\(\log \texttt{kFa}\).

tdg.observable.fermi.momentum_by_kF_squared(ensemble)

\((k/k_F)^2\), which is particularly useful for plotting as a function of momentum.

Bootstraps first, then linearized momentum index \(k\).

Binding Energy

tdg.observable.fermi.binding_by_EF(ensemble)

The binding energy \(-(Ma^2)^{-1}\) divided by the Fermi energy \(k_F^2/2M\),

\[\frac{\mathcal{E}_B}{E_F} = - \frac{2}{(k_F a)^2}\]

Temperature

tdg.observable.fermi.T_by_TF(ensemble)

The temperature in proportion to the Fermi temperature,

\[\frac{T}{T_F} = \frac{1}{\pi \tilde{\beta} N}\]

α

tdg.observable.fermi.alpha(ensemble)

In the language of Ref. [1], \(\alpha(k_F)\) is a dimensionless coupling constant that is the natural expansion parameter of the two-dimensional EFT.