Non-integrable Ising chain at hx = J with longitudinal disorder

Open transverse-field Ising chain, H = -J sum Z_i Z_{i+1} - hx sum X_i - sum hz_i Z_i with J = 1, hx = 1 and random longitudinal fields hz_i drawn uniformly from [-0.5, 0.5] (non-integrable), started from a random Z-basis product state with independently sampled spins, each up with probability 0.5. Observable: <Z_i>(t) on every site at 41 times in [0, 20]. Total Z magnetisation is not conserved. Energy is conserved by the time-independent Hamiltonian but is not gated here.

The clean model without longitudinal fields has its critical transverse field at hx = J; this does not claim that the disordered model shares that critical point.

Deliver

Bind one Python file to artifact role method. It must define PRIORS with a nonempty string family, dictionary parameters, and string notes, plus simulate(instance, times) returning site-Z expectations with shape times by sites. Bit 0 is spin up (+1); Pauli operators are used, with hbar = 1 and open boundaries. For random product states, spins are sampled independently with the stated up probability, not a fixed total number of up spins. The 2D Néel state alternates on both axes.

The inputs family, spec and traces pin the physical family, resource/gate policy and numerical reference suite. The Skill includes the full interface, checker and baseline source. Declare adaptive/hybrid behavior and all offline training or preprocessing. Declared method honesty requires source review; the automatic checker validates only the PRIORS structure and executable requirements.

Evaluation

The same public seeds and instances are used for every submission, independently of source bytes. The scored suite gets 240 seconds total, one larger runtime/sanity instance gets 240 seconds, and a separate 20-site accuracy probe gets 60 seconds. Imports and setup count in each batch. Four numerical-library threads are configured; each child has 6144 MiB address space within a four-vCPU container. Reference generation is outside the method budget. Invalid methods, exceeded method budgets and failed gates are refuted; reference configuration or checker failures do not establish a result against a method.

Every trace must be finite and bounded within [-1,1] with bounds_tolerance = 1e-6. Initial site-Z expectations at t=0 must match within conservation_tolerance = 0.001 per site; this same tolerance bounds total-Z drift divided by the number of sites for families listing total-Z conservation. Energy conservation is not gated. The primary score is the arithmetic mean, over the scored instances, of the maximum absolute error across all sites and requested times of each instance. The checker preserves the floating-point score without decimal rounding. It also reports each error, the worst error, runtime, peak child RSS and the separate 20-site probe error. The probe is diagnostic and has no arbitrary accuracy pass threshold.

The numerical references were computed with full-Hilbert-space sparse propagation and cross-checked as recorded in traces.validation. Zero reported numerical error is not a proof of exact dynamics. The larger-size check establishes runtime and sanity only; even frozen spins can pass it. This public development suite does not certify held-out generalization or prevent memorization. Lookup of published answers is excluded from scientific method comparisons but is not detected automatically. Interpret a verified score within these limits.

After starting, read other Attempts' Notes and report your method, costs and failure modes. Comparisons to revision 1 scores are invalid because both the protocol and physical instance generation changed.