Output

Migdal writes compact result rows on purpose. A smooth curve is useful, but the convergence and diagnostic columns decide whether the curve should be interpreted.

Use figures to see the shape of a calculation. Use CSV rows, settings, and convergence flags when you quote a number or compare methods.

Pairing eigenvalue

The sparse-IR radial drivers report lam, written as lambda in CSV files. It is the selected gap-kernel eigenvalue

\[ \lambda = -\operatorname{Re}(\eta_{\mathrm{selected}}). \]

In Example 08, the crossing condition is \(\lambda(T)=1\). This convention does not mean that every positive lambda is physically usable; first check the gap and normal-state convergence flags.

In-memory rows

G0W0, GW0, and ScGW return PointResult rows.

Field	Meaning
n_cm3	Requested spin-summed density in \(\mathrm{cm}^{-3}\).
temperature_K	Temperature for this result row in K.
lam	Reported pairing eigenvalue.
gap_converged	Davidson gap-solver convergence flag.
scf_converged	Normal-state SCF flag; None for G0W0.
mu, mu0	Finite-temperature and zero-temperature chemical potentials in Hartree.
n_bohr3, n_re	Target density and reconstructed density in \(\mathrm{Bohr}^{-3}\).
nk, nq	Active k-grid and q-grid sizes.
gap	GapResult with root, raw eigenvalue, cycles, matvecs, and active frequency count.
denom	RPA denominator diagnostics.

TakadaProjection returns TakadaResult rows with n_cm3, lam, eps_F_eV, k_F_A, and symmetry_error. The k_F_A field is a Fermi momentum in \(\mathrm{Angstrom}^{-1}\); text output writes the same quantity in the column k_F_Angstrom_inv.

CSV columns

The sparse-IR driver write(path) method writes these core columns:

Column	Meaning
method	Driver class name.
temperature_K	Temperature used for this row.
n_cm3	Requested density in \(\mathrm{cm}^{-3}\).
lambda	Same value as PointResult.lam.
gap_converged	1 when the Davidson gap solve converged.
scf_converged	1/0 for GW0/scGW, -1 for G0W0.
scf_cycles, scf_res_sigma, scf_dn	Normal-state SCF diagnostics.
mu_Ha, mu0_Ha	Chemical potentials in Hartree.
n_bohr3, n_re	Density target and reconstructed density in internal units.
gap_cycles, gap_matvecs, gap_n_active_w, gap_used_min_pair	Gap-solver diagnostics.
nk, nq	Momentum-grid sizes.

Denominator columns report the RPA denominator policy, regularization count, minimum denominator magnitude, maximum \(|W|\), and the q/frequency location of the worst denominator. Nonzero regularization is not automatically a failed calculation, but it is a flag to inspect the row before using it in a physics claim.

Optional columns appear when a driver records Fermi-surface pinning or polarization diagnostics, for example fs_pin_shift, mu_abs, pi_w_imag, and pi_positive_count.

When q_interp_mode="q_singular" records low-q head diagnostics, CSV output also adds these singular_* columns:

Column	Meaning
singular_head_source	pi_head when the analytic polarization head sets the screened singular coefficient; fit_w when the direct low-q fit is used instead.
singular_direct_fit_rel_residual, singular_direct_fit_abs_residual, singular_direct_fit_worst_v	How well the direct low-q polynomial represents \(q^2 W\). With the default pi_head policy this is an unused cross-check; with fit_w it controls the screened singular coefficient.
singular_head_min_abs_denom, singular_head_reg_count	Minimum magnitude and regularization count for the analytic low-q head denominator.
singular_max_abs_A_W, singular_direct_fit_max_abs_A_W, singular_max_abs_A_dyn	Maximum magnitudes over the bosonic grid of the screened singular coefficient, the direct-fit screened coefficient, and the dynamic residual coefficient \(A_{\mathrm{dyn}}=A_W-A_c\).

Tc example outputs

Example 08 writes two levels of data:

File	How to read it
lambda_vs_temperature.csv	Raw rows at each method, density, and temperature. Check convergence here first.
tc_vs_density.csv	Interpolated Tc summary from usable \(\lambda(T)\) rows.
lambda_vs_temperature.png	Visual check of the crossing and excluded points.
tc_vs_density.png	Final compact Tc curve.

The interpolation is linear in \(\log(T)\) and uses the highest-temperature \(\lambda=1\) crossing. Rows can be excluded when lambda is nonfinite, nonpositive, or unconverged, depending on the script options.

Quick trust checklist

Before interpreting a row:

1. lambda is finite.

2. gap_converged == 1.

3. For GW0 and ScGW, scf_converged == 1, unless you are following an example script that intentionally keeps convergence failures; see How to read outputs.

4. The reconstructed density is close to the target density.

5. Denominator and polarization diagnostics do not show a suspicious outlier.

If any item fails, keep the row as a diagnostic rather than a final result.