research-direction: apply HI-NQS-SQD pipeline to non-chemistry physics (lattice, solids, periodic) — niche unexplored space

[thc1006]

TL;DR

99% of SQD/NQS-SCI literature targets molecular chemistry. Lattice models, periodic solids, frustrated magnets, Hubbard model are underexplored with iterative-NQS-driven SQD. This is a thinner literature space — potential niche to add datapoints.

Evidence the niche is open (3+ sources, but limited)

• Symmetry-adapted SQD on lattice (arXiv:2505.00914) — early lattice work, just started
• SQD on cuprate chain (arXiv:2512.04962) — cuprate chain only, scaling-focused
• Evaluating SKQD for Heisenberg models (MDPI 2026) — Heisenberg lattice
• (chemistry has dozens of papers; lattice/solids has maybe 5-10)

Why this might be tractable

1. Lattice Hamiltonians have simpler structure than molecular (mostly 2-body, translation invariant)
2. Symmetries (translation, rotation, particle-hole) reduce effective Hilbert — NQS sampling more efficient
3. Reference values exist for many systems (DMRG, ED, AFQMC)
4. qvartools already has spin Hamiltonian support (hamiltonians/spin/)

Possible target systems

• 2D Hubbard model at half-filling (high-Tc relevance) — DMRG benchmarks at L×4 ladder
• Frustrated J1-J2 Heisenberg — Where DMRG struggles, NQS shines
• Periodic boundary BCS Hamiltonians — pairing physics
• Anderson impurity model — DMFT-style impurity solving with SQD
• Z2 lattice gauge models — non-chemistry quantum field theory

What we'd need to add

1. Hubbard / Heisenberg generators in hamiltonians/spin/ (partial coverage exists)
2. Periodic boundary integrals (k-space basis)
3. Symmetry-adapted basis (translation, point group)
4. NQS architecture suited to lattice (CNN encoder + Transformer decoder?)

Risk

• Other groups may have ongoing unpublished work — must monitor arXiv weekly
• Lattice physics community has different expectations vs. chemistry — peer review more skeptical of NQS
• DMRG often dominates in 1D/quasi-1D — value-add only at higher dimensions

Why bother

• Methodologically transferable — qvartools framework already exists; need new Hamiltonians + benchmarks
• Less crowded vs chemistry — niche workshop paper achievable
• Cross-pollination — lattice insights inform chemistry pipeline (vice versa)

Effort: 2-4 months minimum (substantial new R&D)

• Most work is in implementing new Hamiltonians, not changing pipeline
• Some pipeline tweaks for periodic systems (k-space)

When to do this

Only AFTER:

• Issue research-positioning: HI-NQS-SQD is not a novel method — it's a composition of established techniques. Document accordingly. #50 (positioning audit) confirms chemistry-NQS-SQD is too crowded
• Issue research-direction: cross-method benchmark at fixed compute budget on N2/Cr2 active-space series (only realistic publishable angle) #51 (benchmark study) is published or shelved
• Team has bandwidth (this is exploratory)

Out of scope

• Quantum hardware experiments (different stack)
• Fermionic lattice problems beyond Hubbard (too broad)