[floatingCatty]

What and why

This PR creates one substantive research "start here" article connecting the publicly established work across DeePTB, SLEM, VBCSR, AD-NEGF, and published DeePTB-NEGF/finite-temperature optics applications. It answers a concrete technical question: what still has to happen after a machine-learned Hamiltonian predicts an operator, before one can compute trustworthy observables at scale?

Canonical pages

• English: /research/learned-hamiltonians-to-observables/
• Chinese: /zh/research/learned-hamiltonians-to-observables/

Both have independent original-language prose, visible navigation to the translation, self-canonical, reciprocal hreflang, language-correct BlogPosting metadata, and six original primary citations in JSON-LD. The article is marked Technical perspective / 技术综述, never misrepresented as a peer-reviewed manuscript.

Scientific contents

• Learned Slater–Koster vs. nonorthogonal atomic-orbital operator modeling; generalized Hc=ESc, explicit overlap-metric caveat.
• Correct nonorthogonal Green-function DOS expression, without advocating forming dense inverses. Distinguishes cheap sparse operator action from costly inverse-overlap applications and convergence of response properties.
• The published million-atom GaP DeePTB/TBPM demonstration versus the separate 4,096-atom HSE-trained finite-temperature optical study.
• VBCSR block structure, realistic numerical thresholds, MPI and workload-dependent performance rather than universal speedups.
• Open-system transport and electrode self-energies, 41 nm gated CNT-FET vs. 180 nm zero-bias CNT vs. 2D-material transmission, and differentiable transport as a distinct contribution.
• A concrete five-point validation checklist for models, observables and whole-workflow performance; reproducibility pointers to the existing flower example.

All technical claims link back to the journal/conference articles or public code. No unpublished RSATB result or method is disclosed. No benchmark was newly executed.

Scholarly correction discovered during source verification

The existing 2D DeePTB-NEGF item was labeled only as arXiv:2512.11291 (preprint), but a published IEEE MoSICom 2025 conference paper with DOI 10.1109/MoSICom67153.2025.11398312 now exists (IEEE Xplore online 2 Mar 2026). The bibliography, both research-language notes, both index cards and the maintainer citation audit now reflect the conference publication, while keeping the arXiv source and old publication permalink. It does not claim a journal publication.

Discoverability / maintenance

• Featured link on both research indexes and a restrained bilingual link on the existing homepage; the homepage hero and design are unchanged.
• research.json will automatically expose the two localized URLs as one topic.
• Teach BlogPosting.citation to use a list of multiple verified sources when citation_urls is present (single-citation behavior preserved for existing notes).
• README explains how to add localized technical perspectives; CI audit checks indexes, reciprocal URLs, both JSON-LD citation lists, and IEEE version-of-record metadata.

Merge only after Jekyll Pages build/audit passes and the manuscript-like equations / factual distinctions have been reviewed. Check responsive rendering of tables and math, plus language toggle. This is an author-facing draft, not automatic public publication.

Source references

• DeePTB, Nat. Commun. 15, 6772
• SLEM, ICLR 2025
• VBCSR arXiv:2609.04397
• AD-NEGF PRB 108, 195143
• DeePTB-NEGF npj Comput Mater 11, 375
• Finite-temperature optics npj Comput Mater 12, 268
• DeePTB-NEGF MoSICom 2025 IEEE

Latest automated build verification

GitHub Actions run 38188975408 passed on commit a75d328. GitHub Pages Jekyll built successfully; 403 rendered-site assertions passed across 11 research/technical notes and 11 scholarly records, including both localized guides, source citation arrays, index links, reciprocal hreflang, and the conference DOI/preprint pair.

These tests do not replace author review of the derivations, scientific interpretation, visual rendering of MathJax/table layout, or a post-merge Google crawl.