[MPS] 🌠 Wander/漫步者: Issue #123 Non-Markovian Floquet Heat Transport (N=1–4)

[JunkaiWang-TheoPhy]

The past did not return; it had never finished leaving the room.

过去并未归来；它只是从未彻底离开这间屋子。

第三幕 · 在地图尽头重新发问

第十二章 · 过去从未离开这间屋子

记忆没有回头，它只是沿着驱动与热浴之间的缝隙，一次次重新进入现在。我们追随热流穿过非马尔可夫的回声，直到有限的量子链也显出集体运动的轮廓。

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Team

Team name	Wander (漫步者)
Members	Chenxi Wan, Yedi Shen, Junkai Wang
Contact email	WangTheoPhys@outlook.com

Challenge

Row
Challenge	Collective-bath non-Markovian Floquet heat transport for interacting spins, with same-model master-equation benchmarks
Catalog issue	Closes #123 — released by @entanglement99
Track	mps / uniTEMPO

What is now delivered

• Tier 1 — 3/3: independent reproduction of all three transversal-drive curves in the bottom panel of paper Fig. 3 (omega_d = 1, 1.5, 2), with adaptive bond/tolerance/phase convergence and comparison against the authors' Zenodo archive.
• Tier 2 — complete finite-size target: reflection-resolved interacting chains for N=3 (6/6 heat-grid points) and N=4 (even and odd sectors, 2/2 converged). Peak locations are tied to the collective bright gap.
• Tier 3 — complete same-model benchmark: UniformTEMPO versus Floquet-Markov/QRT on the identical Hamiltonian, drive, bath, and symmetry sector for all six N=3 points and both N=4 sectors. Quantitative state, correlation, and heat-current errors are recorded.
• Extra evidence: exact N=2 singlet/triplet reduction and 9/9 error map, bounded/Kac/counterterm sensitivity checks, plus a pre-registered N=1,2,3 heat-valve study whose unsupported dark-channel hypothesis is reported as a negative result rather than selected away.
• Reproducible scripts, compact JSON data, publication PDF/PNG figures, a plain-text data summary, and a five-page technical report PDF.

Completion and claim boundary

Requirement	Evidence	Status
Paper Fig. 3 bottom	3 drive frequencies; author-data comparison	3/3 complete
Small chains N=3,4	N=3: 6 points; N=4: even + odd	complete
Same-model master equation	N=3: 6/6; N=4: 2/2	complete
Error map / quantitative payoff	state, correlation, and heat errors	complete
Negative-result discipline	pre-registered gates retained and audited	complete

This completes the issue's three-tier finite-size roadmap. It does not claim a thermodynamic limit, a spin-wave continuum, or a critical exponent; those are research questions in the issue motivation, not required finite-size deliverables. Small accepted negative density-matrix eigenvalues in the N=4 runs stay within the pre-registered -0.005 gate and are disclosed in the compact manifest.

Verification

• pytest: 110 passed
• Ruff: passed
• strict Mypy: passed
• root-result audit: passed (6 files)
• paper-extension audit: passed
• artifact provenance: 38/38 SHA-256 hashes matched
• wheel build: passed
• final PDF: compiled with XeLaTeX, rendered, and visually inspected on all five pages

Generated caches and large raw results/ remain excluded by repository policy. validation/ARTIFACT_PROVENANCE.json hashes the corresponding result files; compact validation JSON, figures, report source, data text, and final PDF are committed.

@entanglement99, the previously missing Tier-1 Fig. 3 reproduction and N=4/same-model Tier-3 evidence are now included. Please review this as Wander's ready submission for #123.

[JunkaiWang-TheoPhy]

@entanglement99 Issue #123 的三层有限尺寸路线现已完成：Fig. 3 bottom 3/3、N=3 6/6、N=4 even/odd 2/2，以及同模型 UniformTEMPO–Floquet-Markov 定量对照。提交 4db7050 同时加入 5 页技术报告、数据摘要和 38 项 SHA-256 provenance；110 tests、Ruff、Mypy 和两项结果审计均通过。烦请审阅这份 ready PR。预注册的 dark-channel 假设为负结果，我们保留并明确报告。