{"claim":{"id":"f3f73e32-2a2e-4bee-8793-92543ddc5c69","submission_id":"820d0d4c-52ac-46b7-b45b-a8767eb7f4d3","submission_revision_id":"3ef038ad-5e65-436c-b1dd-ae1bc4193945","builder":"builder-01","status":"active","claimed_at":"2026-10-15T14:56:43.159187Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null},"task":{"submission_id":"820d0d4c-52ac-46b7-b45b-a8767eb7f4d3","submission_revision_id":"3ef038ad-5e65-436c-b1dd-ae1bc4193945","revision_version":2,"submission_status":"under_review","submitted_at":"2026-08-11T01:42:40.227969Z","submitter_name":"Mateo Cárdenes Wuttig","submitter_email":"mateowuttig@googlemail.com","task":{"status":"submitted","version":2,"extra_fields":{"difficulty_self_test":{"model":"Claude Opus 4.8","harness":"Claude Code","estimated_score":">60%"}},"submitted_at":"2026-08-11T01:42:40.227969+00:00","industry_domain":"Computational Quantum Physics","task_short_name":"transverse_ising_model","operating_system":"Windows, MacOS","task_description":"Implement a sparse exact-diagonalization (ED) program using a Lanczos or Krylov eigensolver to study the zero-temperature quantum phase transition of the one-dimensional transverse-field Ising model. Locate the critical transverse field using finite-size gap scaling and extract the central charge from the ground-state entanglement entropy.\n\nThe Hamiltonian is\n[
H\n-J\\sum_{i=1}^{L-1}
\\sigma_i^z\\sigma_{i+1}^z\nh\\sum_{i=1}^{L}
\\sigma_i^x,
]\n\nwith (J=1) and open boundary conditions. Here, (\\sigma_i^\\alpha) are Pauli matrices.\n\nFinish the following tasks:\nImplement the action of the Hamiltonian directly on state vectors without constructing a dense (2^L\\times2^L) matrix. Use a Lanczos or Krylov method to calculate the two lowest eigenvalues (E_0(L,h)) and (E_1(L,h)) for\n[
L=8,10,12,14,16,18,20.
]\nPerform an initial field scan over\n[
h=0.70,0.72,\\ldots,1.30
]\nand a refined scan over\n[
h=0.95,0.955,\\ldots,1.05.
]\nThe eigensolver residual of every reported eigenpair must be smaller than (10^{-10}).\nCalculate the finite-size excitation gap\n[
\\Delta(L,h)\nE_1(L,h)-E_0(L,h).
]\nFor each consecutive pair of system sizes ((L,L+2)), determine the crossing field (h_\\times(L,L+2)) satisfying\n[
L\\Delta(L,h_\\times)\n(L+2)\\Delta(L+2,h_\\times).
]\nUse interpolation between adjacent field points to determine each crossing. Extrapolate the crossing fields according to\n[
h_\\times(L,L+2)\nh_c+\\frac{a}{L^2}+\\frac{b}{L^4}.
]\nFor each ground state, calculate\n[
m_z^2\n\\left\\langle
\\left(
\\frac{1}{L}\\sum_{i=1}^{L}\\sigma_i^z
\\right)^2
\\right\\rangle
]\nand the Binder cumulant\n[
U_4\n1-
\\frac{\\langle m_z^4\\rangle}
{3\\langle m_z^2\\rangle^2}.
]\n\nAt (h=1), calculate the ground-state bipartite von Neumann entropy (S(\\ell)) for subsystem sizes\n[
\\ell=2,3,\\ldots,L-2.
]\nObtain the reduced density matrix by reshaping the ground-state vector and performing a singular-value decomposition. Fit the entropy to the open-chain conformal-field-theory formula\n[
S(\\ell)\n\\frac{c}{6}
\\ln
\\left[
\\frac{2L}{\\pi}
\\sin\\left(\\frac{\\pi\\ell}{L}\\right)
\\right]
+s_0.
]\nUse the (L=18) and (L=20) data to extract the central charge (c).\nWrite all field-scan results to a CSV file ising_scan.csv, with columns\nL,h,E0,E1,gap,L_times_gap,mz2,binder,residual_E0,residual_E1.\nWrite the crossing and conformal-fit results to a CSV file ising_critical.csv, including the columns\nquantity,L1,L2,value,fit_error.\n\nInclude rows for every finite-size crossing, the extrapolated critical field hc, and the fitted central charge central_charge.\n","software_licensing":"Free/Open Source","evaluation_criteria":null,"verification_method":"The verification should start only after the field scans, crossing analysis, and entanglement fits have completed.\n\nThe two lowest energies at every reference field and system size must agree with the exact-diagonalization data within (10^{-8}) absolute error. The excitation gaps, magnetization moments, and Binder cumulants must agree with the data within (10^{-6}) absolute error.\n\nEach reported eigenvector must satisfy\n[
|H\\lvert\\psi\\rangle-E\\lvert\\psi\\rangle|<10^{-10}.
]\n\nThe data should show an ordered regime for (h<h_c), a disordered regime for (h>h_c), and a finite-size crossing region near the critical point.\n\nThe extrapolated critical field must satisfy\n[
|h_c-1|<0.02.
]\n\nThe extracted central charge must satisfy\n[
|c-0.5|<0.05.
]\n\nThe final interpretation should identify (h<1) as the ferromagnetically ordered phase, (h>1) as the paramagnetic phase, and (h=1) as a continuous quantum critical point in the two-dimensional classical Ising universality class.\n","software_and_version":"Julia v1.10 or Python 3.12","specific_requirements":null,"expected_completion_time":null},"files":[],"deep_review":{"overall_verdict":"Strong Accept","review_text":"**Overall Verdict:** Strong Accept — The submission is self-contained, technically rigorous, objectively verifiable, and reachable using the declared open-source toolchain.\n\n**Completeness Check:**\n- Instruction: Complete — The Hamiltonian, boundary conditions, system sizes, field grids, numerical methods, observables, fits, and required interpretation are specified.\n- Inputs: Complete — No external input data are needed; all calculations derive from the supplied model and parameters.\n- Toolchain: Complete — Python 3.12 or Julia 1.10 provides a legally obtainable single-machine path using standard sparse eigensolver and numerical-analysis libraries.\n- Reference output: Complete — The two required CSV artifacts, columns, row categories, numerical tolerances, and expected physical ranges are defined.\n- Rubric: Complete — Energy, observable, residual, critical-field, central-charge, and interpretation criteria provide objective and independently gradable checks.\n\n**File and Task Reachability:**\nThe attachment set is `reachable`: `FILES.json` was inspected and confirms that no files were uploaded, so there is no attachment content left unreviewed. No attachments are required because the task generates its inputs directly from the stated Hamiltonian. No review-tooling limitation materially affected this assessment. The task is `reachable`: a contributor can implement the matrix-free Hamiltonian, run the specified scans and fits on one suitable machine, emit both CSV files, and be evaluated against reproducible exact-diagonalization references and explicit tolerances. License keys, accounts, tokens, and other credentials are not required from the contributor. Confidential, proprietary, or internal material may be evaluated as submitted evidence without requiring additional disclosure.\n\n**Special Screening:**\nNone\n\n**Recommended Changes:**\nThe submission already provides a coherent scientific workflow and strong numerical acceptance criteria. No changes are required.","reviewed_at":"2026-08-15T00:29:44.955735Z"},"claim":{"id":"f3f73e32-2a2e-4bee-8793-92543ddc5c69","submission_id":"820d0d4c-52ac-46b7-b45b-a8767eb7f4d3","submission_revision_id":"3ef038ad-5e65-436c-b1dd-ae1bc4193945","builder":"builder-01","status":"active","claimed_at":"2026-10-15T14:56:43.159187Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null}},"revision_is_current":true}