Bertaina and Giorgini, Phys. Rev. Lett. 106, 110403 (2011)

Ref. [20] uses fixed-node diffusion Monte Carlo.

Table I provides energies with uncertainties.

Figure 4 shows the contact density \(c/k_F^4\). The data were provided by Gianluca Bertaina.

tdg.references.PRL106110403.table_I()[source]

Note that Fig. 2 shows 18 points but Table I gives only 16 rows.

Returns

torch.tensor

Return type

The rows are \(\ln(k_F a_{2D})\), \(E/E_{FG}\), the uncertainty on \(E/E_{FG}\), and half the binding energy \(\mathcal{E}_B\).

tdg.references.PRL106110403.conventional_table_I()[source]

The same as table_I() but converted from the geometric convention.

tdg.references.PRL106110403.figure_4()[source]

Figure 4 of Ref. [20] provides measurements of contact_by_kF4() as a function of \(\log k_F a_{2D}\).

Returns the data from Figure 4, in TWO tensors, the first with BCS data and the other with JS data. Each tensor has \(\log k_F a_{2D}\) in the first row, \(c/k_F^4\) in the second, and the uncertainty on \(c/k_F^4\) in the third.

The data were provided by Gianluca Bertaina.

tdg.references.PRL106110403.c0_by_kF4(eta)[source]

Explained just above Figure 3, \(c_0\) is ‘the contribution to the contact from the molecular state’.

Parameters

eta (torch.tensor) – \(\eta = \log k_F a_{2D}\)

Returns

The two-body contribution to the contact at \(\eta\).

Return type

torch.tensor

tdg.references.PRL106110403.figure_4_fit(eta)[source]

Figure 4 of Ref. [20] shows a fit of contact_by_kF4() as a function of \(\log k_F a_{2D}\).

The fit parameters were provided by Gianluca Bertaina.

Parameters

eta (torch.tensor) – \(\eta = \log k_F a_{2D}\)

Returns

\(c/kF^4\) at \(\eta\).

Return type

torch.tensor

tdg.references.PRL106110403.figure_4_reproduction(ax)[source]

Reproduce Figure 4 of Ref. [20] relying on data in figure_4() and the figure_4_fit().

import matplotlib.pyplot as plt
fig, ax = plt.subplots(1,1, figsize=(6,4))

from tdg.references import PRL106110403
ax, inset = PRL106110403.figure_4_reproduction(ax)

(Source code, png, hires.png, pdf)

../_images/PRL106110403-1.png
Parameters

ax (matplotlib.Axes) – Where to draw the figure.

Returns

  • ax (matplotlib.Axes) – The same handle given, but with art.

  • inset – A handle for the inset.

tdg.references.PRL106110403.conventional_figure_4()[source]

The same data as figure_4() but with \(\log k_F a\) rather than \(\log k_F a_{2D}\).

tdg.references.PRL106110403.energy_comparison(ax, **kwargs)[source]

The first column of Table I gives \(E/E_{FG}\) . To get a fair comparison we need to subtract \(E_{MF}/E_{FG} = (1+\alpha)\).

tdg.references.PRL106110403.contact_comparison(ax, include_all=False, **kwargs)[source]

Many of the points are off-scale compared to the contact comparison in Ref. [1].

Plots the JS-DMC contact from Ref. [20] on the axis ax and plots the BCS-DMC contact only if include_all.