{"claim":{"id":"8e1bc4d0-ea36-4026-ac71-9160a1dd0f21","submission_id":"4d255c50-abf1-4d01-b8f2-35ba48df631e","submission_revision_id":"b194fcea-48b0-4fb8-a148-1423f28ed6ab","builder":"builder-01","status":"active","claimed_at":"2026-10-15T14:56:36.578283Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null},"task":{"submission_id":"4d255c50-abf1-4d01-b8f2-35ba48df631e","submission_revision_id":"b194fcea-48b0-4fb8-a148-1423f28ed6ab","revision_version":1,"submission_status":"under_review","submitted_at":"2026-08-10T13:14:16.615887Z","submitter_name":"Mateo Cárdenes Wuttig","submitter_email":"mateowuttig@googlemail.com","task":{"status":"submitted","version":1,"extra_fields":{"difficulty_self_test":{"model":"Opus 4.8","harness":"Claude Code","estimated_score":">60%"}},"submitted_at":"2026-08-10T13:14:16.615887+00:00","industry_domain":"Computational Quantum Physics","task_short_name":"hubbard_chain_dynamics","operating_system":"MacOS","task_description":"Implement a Julia matrix-product-state (MPS) program using ITensorMPS.jl to simulate the real-time dynamics of a half-filled, noninteracting one-dimensional Fermi-Hubbard chain. Validate the MPS time evolution against the exact free-fermion solution, which is obtained from diagonalizing the Hamiltonian in momentum space, and determine whether the initially imposed charge-density wave persists or relaxes.\n\nThe Hamiltonian is\n\n[
H =
-t_{\\mathrm{hop}}
\\sum_{i=1}^{L-1}\\sum_{\\sigma=\\uparrow,\\downarrow}
\\left(
c_{i\\sigma}^{\\dagger}c_{i+1,\\sigma}
+
c_{i+1,\\sigma}^{\\dagger}c_{i\\sigma}
\\right)
+
U\\sum_{i=1}^{L}n_{i\\uparrow}n_{i\\downarrow},
]\n\nwith open boundary conditions, in units of t_{\\mathrm{hop}}=1, and U=0 (non-interacting spinful fermions). Here, c_{i\\sigma} (c_{i\\sigma}^{\\dagger}) destroys (creates) an electron on site i=1,…,L of spin \\sigma = \\uparrow, \\downarrow. \n\nUse an initial charge-density-wave (CDW) product state\n\n[
\\lvert\\psi_0\\rangle\n\\prod_{\\substack{i=1\\ i\\ \\mathrm{odd}}}^{L}
c_{i\\uparrow}^{\\dagger}c_{i\\downarrow}^{\\dagger}
\\lvert 0\\rangle,
]\n\nsuch that odd sites are doubly occupied and even sites are empty. The total particle number is N=L and is conserved.\n\nFinish the following tasks:\n\nImplement second-order Trotter time evolution using nearest-neighbor two-site gates. Perform simulations for different lengths (L=16,32,48), from time (t=0) to (t=3.0), with time step (\\Delta t=0.025). Use an SVD truncation cutoff of (10^{-10}) and a maximum MPS bond dimension of at least 2000.\n\nIndependently calculate the exact dynamics by diagonalizing the single-particle hopping matrix. For each spin species, evolve the one-particle correlation matrix according to\n[
C_{\\sigma}(t)\ne^{-iht}C_{\\sigma}(0)e^{iht},
]\nwhere (h) is the (L\\times L) single-particle hopping matrix. Use this correlation matrix to calculate the exact local densities and half-chain entanglement entropy.\nAt times (t=0,0.1,\\ldots,3.0), calculate:\nthe local total density
[
n_i(t)=
\\langle n_{i\\uparrow}+n_{i\\downarrow}\\rangle;
]\nthe charge-density-wave imbalance
[
\\mathcal I(t)
\\frac{1}{L}
\\sum_{i=1}^{L}
(-1)^{i+1}n_i(t);
]\nthe bipartite von Neumann entropy across the central bond,
[
S_{L/2}(t)
-\\operatorname{Tr}\\rho_{1,\\ldots,L/2}(t)
\\ln\\rho_{1,\\ldots,L/2}(t).
]\nFor the exact calculation, obtain the entanglement entropy from the eigenvalues (\\nu_a) of the correlation matrix restricted to the left half of the chain:\n[
S_{L/2}\n-\\sum_a
\\left[
\\nu_a\\ln\\nu_a
+
(1-\\nu_a)\\ln(1-\\nu_a)
\\right].
]\nBoth spin species must be included.\n\nWrite the results to a CSV file: free_hubbard_dynamics.csv. Each row should correspond to one system size and one time. Include the columns\nL,time,mps_imbalance,exact_imbalance,mps_entropy,exact_entropy,max_density_error,discarded_weight,max_bond_dimension.\nHere,\n\n[
\\text{max_density_error}\n\\max_i
\\left|
n_i^{\\mathrm{MPS}}-n_i^{\\mathrm{exact}}
\\right|.
]\n\nFor each individual SVD truncation, define the discarded weight as\n\\frac{
\\sum_{\\alpha\\in\\mathrm{discarded}}s_{\\alpha}^{2}
}{
\\sum_{\\alpha}s_{\\alpha}^{2}
}.
]\n\nThe implementation should exploit particle-number conservation. \n","software_licensing":"Free/Open Source","evaluation_criteria":null,"verification_method":"The verification should begin only after the MPS and exact calculations have both completed.\n\nWrite the results to\nresults/free_hubbard_dynamics.csv.\n\nEach row must correspond to one system size and one stored time. Include the columns\nL,time,mps_imbalance,exact_imbalance,mps_entropy,exact_entropy,max_density_error,discarded_weight,max_bond_dimension.\n\nThe column discarded_weight must contain the largest discarded weight encountered in any two-site SVD from (t=0) up to and including the current output time. Its value at (t=0) must be zero.\n\nThe column max_bond_dimension must contain the largest bond dimension present in the MPS at the corresponding output time.\n\nThere are (31) stored times for each of the three system sizes. The completed CSV file must therefore contain (93) data rows in addition to its header.\n\nFor every stored time and system size:\nthe absolute MPS error in the imbalance must be smaller than (2\\times10^{-3});\nthe absolute MPS error in the half-chain entropy must be smaller than (10^{-2});\nmax_density_error must be smaller than (5\\times10^{-3}).\n\nThe implementation must exploit particle-number conservation.\n\nThe final imbalance at (t=3) must be smaller than its initial value for every system size, demonstrating relaxation of the initial charge-density modulation.\n","software_and_version":"Julia v1.10, ITensorMPS.jl","specific_requirements":null,"expected_completion_time":null},"files":[],"deep_review":{"overall_verdict":"Strong Accept","review_text":"**Overall Verdict:** Strong Accept — The submission is complete, technically coherent, objectively verifiable, and feasible on a suitable single machine using the specified open-source toolchain.\n\n**Completeness Check:**\n- Instruction: Complete — The Hamiltonian, boundary conditions, initial state, system sizes, time grid, Trotter order, truncation controls, observables, and conservation requirement are specified.\n- Inputs: Complete — No external input data are needed; the hopping matrix and initial state are fully determined by the analytical specification.\n- Toolchain: Complete — Julia 1.10 and ITensorMPS.jl provide a legally obtainable implementation path on macOS.\n- Reference output: Complete — The required CSV path, schema, row count, time points, aggregation semantics, and numerical accuracy thresholds establish a sufficient output contract.\n- Rubric: Complete — Success is objectively measurable through row count, conservation use, error tolerances, discarded-weight semantics, bond dimensions, and final-imbalance relaxation.\n\n**File and Task Reachability:**\nThe attachment set is **reachable**. `FILES.json` was inspected and contains no uploaded attachments, so no files required downloading, no attachment content remains unreviewed, and there are no attachment-related tooling limitations. The task is **reachable** end to end: a contributor can construct all inputs from the specification, run both the QN-conserving MPS and exact free-fermion calculations, produce the 93-row CSV, and evaluate it against explicit numerical criteria. The reference to momentum-space diagonalization is compatible with diagonalizing the open-chain single-particle hopping matrix into its eigenmode basis and does not obstruct implementation. 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 defines a substantial professional computational-physics workflow with deterministic inputs and rigorous validation criteria. No changes are required.","reviewed_at":"2026-08-15T00:27:43.561904Z"},"claim":{"id":"8e1bc4d0-ea36-4026-ac71-9160a1dd0f21","submission_id":"4d255c50-abf1-4d01-b8f2-35ba48df631e","submission_revision_id":"b194fcea-48b0-4fb8-a148-1423f28ed6ab","builder":"builder-01","status":"active","claimed_at":"2026-10-15T14:56:36.578283Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null}},"revision_is_current":true}