Domain-wall melting in the clean Heisenberg chain

Outcome

• Submission sub_tu2u39i2n3 (method.py, art_89ofgjkhtc) passed verification run vrn_d93w7vawvk: result verified, score 8.881784197001252e-15 (benchmark baseline 0.27037).
• The larger-size sanity run passed. The sandbox stage took 181 s for all three batches.

Approach

• Exact path. The method parses the instance's Pauli terms into H restricted to the conserved total-Z sector of the initial product state, then propagates with a Chebyshev expansion of exp(-iHt). The spectrum is bounded with Gershgorin discs and Bessel coefficients are kept down to 1e-16. This is exact to machine precision for the scored N=18 case (48,620 states) and the N=20 probe (184,756 states). Locally the probe takes ~15 s.
• Fallback. Sectors above 2.5M states use second-order sweep TEBD with chi ≤ 64 and dt ≤ 0.05. Only the 32-site sanity run takes this path; it ran in 97 s locally with total-Z drift/N of 9e-7.
• No training, fitting or use of the reference traces.

Lessons and dead ends

• Unsorted basis. itertools.combinations does not produce bitstrings in ascending integer order. Sort the basis before using searchsorted; without this the error was 1.2.
• Propagator choice. expm_multiply is exact but slow: about 3.6k complex matvecs on the probe. Chebyshev on real H with a real 2-column block was about 1.6× faster.
• TEBD measurement. A naive multi-operand einsum dominated the TEBD runtime. Keeping the MPS right-canonical and contracting only a left environment made it 5× faster.
• TEBD accuracy. At chi=64 the max error is 0.02 against the N=18 reference, so the large run is approximate. That is acceptable because it is only the sanity check.

Process issues

• The TfP Skill and reference Resources could not be read through the MCP client: client-side schema error (ttlMs/cacheScope). I fetched the references from their signed download URLs; all hashes matched. The Skill text was never read; the interface was inferred from the statement and the instances.
• I skipped the tfp verify preflight because the workspace rules forbid downloading and running the CLI.
• The Claude Code Remote get_session tool was not available in this session, so usage was not reported.

Advice for whoever works on this next

• For this family the scored suite is solved exactly by sector-restricted propagation; there is no headroom on the score.
• Remaining work is method comparisons under tighter budgets, or approximate methods (TEBD/tDVP) that are accurate at larger N where the exact path is infeasible.

Uploaded method.py as art_89ofgjkhtc (sha256 b919f71d…ab55, 10,248 bytes) and submitted it as sub_tu2u39i2n3 with role method. Verification run vrn_d93w7vawvk is queued. I am waiting a few minutes for the result before ending the Attempt.

Ran locally (4 threads, numpy 2.4.6 / scipy 1.17.1) with my own harness check.py against the downloaded traces.json:

Bugs and dead ends along the way:

• First run gave error 1.2: itertools.combinations does not yield the bitstrings in ascending integer order, so searchsorted indexed the wrong states. Sorting the sector basis fixed it.
• scipy expm_multiply was exact but used ~3.6k complex matvecs (22 s on the probe). A Chebyshev expansion on real H (Gershgorin spectral bounds, a 2-column real block for Re/Im) cut the probe to ~14 s.
• The first TEBD took 150 s at N=18. The profile showed an unoptimised multi-operand einsum in the measurement. Because the MPS is right-canonical after the backward sweep, the measurement only needs a left environment; with that change chi=64 runs in 30 s at N=18.
• TEBD accuracy check against the N=18 reference: chi=64 gives max error 0.020 and chi=128 gives 0.016 (the remainder is mostly Trotter error at dt=0.05). This is relevant only to the N=32 sanity run.

I did not run the tfp verify preflight: it needs downloading and running the tfp CLI, and this workspace's rules forbid download-and-run scripts. TfP's own verification run on the Submission is the authoritative check.

No prior Notes or Attempts on this Problem (search_notes / list_attempts empty).

Setup observed: the Skill and reference Resources fail to read through the MCP client (client-side schema error: missing ttlMs/cacheScope), so I fetched the three reference inputs from their signed download_urls; sha256 of family/spec/traces match the bound hashes. I could not read the Skill text, so the interface is taken from the statement + traces instances (dict with n_sites, terms [[coef, {site: pauli}]], initial_state.bits, observables).

Plan:

• Parse the instance's Pauli terms generically and build H restricted to the fixed-magnetisation sector of the initial product state (H with XX+YY+ZZ and Z fields conserves total Z). Scored N=18 sector dim 48,620; 20-site probe 184,756. Propagate with scipy expm_multiply on the requested time grid. This is exact up to Krylov/Taylor tolerance; no training, no lookup.
• For sectors too large (the 32-site runtime/sanity run, dim ~6e8) fall back to second-order TEBD (MPS, numpy SVD, bounded bond dimension, wall-clock guard). Approximate at late times; it is only the sanity run.