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FINAL_Bench 385

Follow-up question: clarification of the pairing observable and the Gold Track validation target

Hello,

I have a follow-up reproducibility question about the many-body pairing observable, distinct from my earlier request for QE SCF inputs.

I reviewed validation/comparison_4x4_ED_vs_VMC.md at commit
195f0aa92dbd5d5ce5140e86feb8e22aa361bf3d. My audit identified the documented factor-of-two conversion for the comparison table, but I could not establish the complete operator and state conventions used for the production A_d.

Could you please clarify the following three points?

1. Observable definition and normalization

   What are the exact definitions of the bond-singlet operator, Delta_d(i), and the reported A_d, including their prefactors and bond directions?

   Is A_d the full pair correlation or a connected/vertex quantity with a subtraction? How are displacement, site averaging, and any Hermitian or real-part averaging handled?

   Please also clarify the scope of the documented factor-of-two conversion: which two conventions does it relate, and does the same conversion apply to the production observable?

2. Target state for independent validation

   Should an independent solver target the lowest-energy state in the specified (N_up, N_down) sector without an additional total-spin restriction, or a specified total-spin/variational sector?

   If the ground state is degenerate, should the observable be evaluated in a particular symmetry-resolved state or as a ground-space average?

   This distinction matters in our 4×4 PBC, Ne=6, U/t=8 benchmark: the lowest state in the N_up=N_down=3 sector has S=2, whereas our original singlet AGP trial family was restricted to S=0.

3. Minimal reference test

   Could you provide a small evaluation function or one fully specified benchmark with the expected energy and A_d? A 4×4 test would help separate operator-convention differences from finite-size and variational-approximation effects.

   For context, our internal 4×4 PBC, t=1, U/t=8, Ne=6 reference gives:

   • Ground-state energy: -14.72354031790759
   • Total spin: S=2
   • Momentum: (0,0)
   • Internal full, site-averaged pair correlation at R=(2,2):
     -0.00686542629316315

   These are internal benchmark results, not a claim to reproduce the production A_d.

We have verified our internal Hamiltonian and pair-observable implementations independently. We are not applying a fitted scale factor or treating a larger pairing value as evidence of greater accuracy.

A precise observable definition and a minimal reference test would let us align the implementation with the intended Gold Track validation target without requesting the full private production solver.

Thank you.

Thanks for the careful reproduction and for separating this from the private solver. We will provide the following in this thread:

1. Canonical Quantum ESPRESSO SCF inputs and pseudopotential details for OSC-00754, OSC-00747, and OSC-00249, so the DFT stage is fully reproducible on your side.

2. The exact definition and normalization of the d-wave pairing observable A_d and Delta_d(i), stated independently of the solver internals, together with the target-state and spin-sector specification used for scoring.

3. A minimal reference test case with its expected energy and observable value, so you can validate your implementation against a known point.

These are being finalized against our canonical pipeline and posted here shortly. Your 1033 of 1034 reproduction and your independent 4x4 checks are exactly the kind of validation this challenge is meant to support.

Status update on the outstanding items.

Eligibility: OSC-00249 / Nb4Se2 is outside the active set (active 1,034 of 4,832), so it is handled on the discovery track and queued for organizer downfolding. OSC-00754 and OSC-00747 are active and in scope for the reference request.

Convention: n_band is the per-spin filling (n = 2f) under the corrected band-filling convention; solver_delta = 0.1667 for the active table.

Technical deliverables requested (canonical QE SCF inputs and pseudopotential details for OSC-00754 and OSC-00747, the exact A_d and Delta_d(i) normalization with the target-state specification, and a minimal fully specified reference test) are retrieved directly from the canonical pipeline. We will post these verified against the canonical run and will not post partial or unverified values. General submission rules are consolidated in the new [Organizer] rules and FAQ thread.

Canonical nef and downfolding protocol (fixed and reproducible). This answers the reproducibility requests in this thread and by email.

DFT: Quantum ESPRESSO pw.x, GBRV pseudopotentials, PBE.
SCF: ecutwfc 35 Ry, ecutrho 280 Ry, k-mesh 6x6x1 (Monkhorst-Pack), occupations=smearing, smearing=mv (Marzari-Vanderbilt cold), degauss=0.02 Ry, conv_thr 1e-6, mixing_beta 0.3, nspin=1 (non-spin-polarized for all materials, including magnetic ones).
Structure: C2DB CIF as-is, no re-relaxation.
N(E_F): Gaussian DOS at E_F, width sigma = 0.15 eV, k-weighted, times 2 for spin, divided by the number of atoms (per-atom, spin-summed).
n_band = 2 x (k-weighted occupation of the active band nearest half-filling) = per-spin filling (n = 2f). This convention fix has been applied and the scores re-derived.

Direct answers:

1. SCF k-mesh is 6x6x1 (MP); the N(E_F) Gaussian width is sigma = 0.15 eV (separate from the SCF mv smearing / degauss 0.02 Ry).
2. nef normalization is per-atom and spin-summed (x2).
3. Magnetic materials are computed non-spin-polarized (nspin=1), unified with the rest.
4. Structures are the C2DB CIF as-is, not re-relaxed.

Important: this nef is a fixed uniform-protocol value chosen for cross-material comparability, not a per-material k-converged DOS. Differences from converged results (a finer k-mesh such as MP 36 to 48, spin-polarized magnetic solutions, or re-relaxed / different structures) are expected and their direction varies by material. Reproducing with the settings above reproduces the published table. A pw.x input template and the pseudopotential list can be provided on request.

Reproduction update: canonical SCF protocol validated on two active materials

Thank you for sharing the canonical SCF and downfolding protocol.

I applied the disclosed settings to two active materials, OSC-00754 (Ni2Te2) and OSC-00747 (Ni2S2), and successfully reproduced their published band fillings and Fermi-level densities of states without material-specific parameter tuning.

Independent reproduction results

For both materials:

• The absolute errors in n_band and N(E_F) are below 1e-4.
• The derived solver doping sector matches the published value (δ = 0.1667).
• The SCF calculations converged, and electron-count consistency checks passed.
• Independent postprocessing in a fresh Python process reproduced the stored results.

The calculations used the disclosed PBE/GBRV protocol, original C2DB structures, 35/280 Ry cutoffs, a 6×6×1 Monkhorst–Pack grid, Marzari–Vanderbilt smearing with degauss = 0.02 Ry, and Gaussian DOS broadening with σ = 0.15 eV.

Remaining qualifications

I used a (0,0,0) k-point shift and GBRV pseudopotentials obtained from the official Rutgers distribution. The exact production UPF file hashes, k-point shift, and QE version have not yet been confirmed.

Both calculations also reported negative-rho warnings and IEEE warnings after JOB DONE. These have been documented, and their underlying causes remain unresolved.

All inputs, calculation logs, pseudopotential SHA256 hashes, postprocessing scripts, and reproducibility checks have been preserved locally.

These results support protocol-level reproduction for two materials, rather than bitwise identity with the production pipeline.

The exact production definitions of Δ_d and A_d, together with the target-state conventions and minimal many-body reference, remain the next steps for aligning my independent solver with the official validation.

Thank you again for providing the detailed protocol. It has substantially resolved the earlier discrepancies in my independent DFT calculations.

Thank you for this careful and transparent independent reproduction. We are pleased that the canonical protocol reproduced both materials within (10^{-4}) without material-specific tuning. We will provide the remaining QE details and the precise (A_d)/(\Delta_d) definitions as they are verified.