{ "schema": { "name": "qft.quantum-information.tilted-ising-membrane-transfer", "version": 1, "id": "qft.quantum-information.tilted-ising-membrane-transfer.v1", "top_level_fields": [ "schema", "claim_boundary", "metadata", "model", "initial_state", "data_split", "numerics", "fit", "held_out_geometry", "adversary", "prehydrodynamic_control", "convergence", "validation", "records" ], "record_fields": [ { "name": "schema_version", "type": "string", "unit": "none", "description": "Record schema identifier." }, { "name": "time_J_inverse", "type": "number", "unit": "J^-1", "description": "Evolution time with J=hbar=1." }, { "name": "primary_fit_window", "type": "boolean", "unit": "none", "description": "True exactly for the ten primary fit times from 1.2 through 3.0." }, { "name": "primary_chaotic_cut_x6_nats", "type": "number", "unit": "nat", "description": "Raw entropy across cut x=6." }, { "name": "primary_chaotic_cut_x7_nats", "type": "number", "unit": "nat", "description": "Raw entropy across cut x=7." }, { "name": "primary_chaotic_cut_x8_nats", "type": "number", "unit": "nat", "description": "Raw entropy across cut x=8." }, { "name": "primary_chaotic_cut_x9_nats", "type": "number", "unit": "nat", "description": "Raw entropy across cut x=9." }, { "name": "primary_chaotic_cut_x10_nats", "type": "number", "unit": "nat", "description": "Raw entropy across cut x=10." }, { "name": "primary_chaotic_cut_mean_nats", "type": "number", "unit": "nat", "description": "Mean of the five raw central-cut entropies used for the fit." }, { "name": "primary_chaotic_interval_l8_nats", "type": "number", "unit": "nat", "description": "Held-out centered eight-site interval entropy in the chaotic chain." }, { "name": "frozen_interval_l8_prediction_nats", "type": "number", "unit": "nat", "description": "Frozen two-boundary prediction clip(2(c+r t),0,8 ln 2)." }, { "name": "primary_chaotic_interval_l8_residual_nats", "type": "number", "unit": "nat", "description": "Chaotic direct full-state entropy minus the frozen prediction." }, { "name": "primary_integrable_interval_l8_nats", "type": "number", "unit": "nat", "description": "Centered eight-site interval entropy at the matched-energy integrable point." }, { "name": "primary_integrable_interval_l8_residual_nats", "type": "number", "unit": "nat", "description": "Integrable direct full-state entropy minus the frozen chaotic prediction." }, { "name": "control_dt001_chaotic_cut_x8_nats", "type": "number", "unit": "nat", "description": "L=16 chaotic central-cut result with dt=0.01." }, { "name": "control_dt001_chaotic_interval_l8_nats", "type": "number", "unit": "nat", "description": "L=16 chaotic interval result with dt=0.01." }, { "name": "control_L18_chaotic_cut_x9_nats", "type": "number", "unit": "nat", "description": "L=18 chaotic central-cut result with dt=0.02." }, { "name": "control_L18_chaotic_interval_l8_nats", "type": "number", "unit": "nat", "description": "L=18 chaotic interval result with dt=0.02." }, { "name": "primary_chaotic_energy_density", "type": "number", "unit": "J/site", "description": "Energy density during the primary chaotic evolution." }, { "name": "primary_integrable_energy_density", "type": "number", "unit": "J/site", "description": "Energy density during the primary integrable evolution." }, { "name": "control_dt001_chaotic_energy_density", "type": "number", "unit": "J/site", "description": "Energy density in the dt=0.01 control." }, { "name": "control_L18_chaotic_energy_density", "type": "number", "unit": "J/site", "description": "Energy density in the L=18 control." }, { "name": "primary_chaotic_norm_error", "type": "number", "unit": "none", "description": "Absolute deviation of the primary chaotic state norm from one." }, { "name": "primary_integrable_norm_error", "type": "number", "unit": "none", "description": "Absolute deviation of the primary integrable state norm from one." }, { "name": "control_dt001_chaotic_norm_error", "type": "number", "unit": "none", "description": "Absolute norm deviation in the dt=0.01 control." }, { "name": "control_L18_chaotic_norm_error", "type": "number", "unit": "none", "description": "Absolute norm deviation in the L=18 control." } ], "additional_top_level_fields_allowed": false, "additional_record_fields_allowed": false }, "claim_boundary": { "machine_label": "determines_E_at_zero_slope_only_not_full_E_of_v", "reader_facing": "This benchmark determines only the zero-slope membrane datum E(0) from homogeneous product-state cut growth. It neither infers nor validates the full line-tension function E(v).", "intercept_scope": "The fitted intercept is a finite-time per-boundary correction, not part of the asymptotic membrane tension." }, "metadata": { "title": "Tilted-Ising zero-slope membrane geometry transfer", "description": "A deterministic finite-chain calculation that fits E(0) from single-cut growth, freezes the result for an eight-site interval, and applies the same fit without refitting to integrable and prehydrodynamic controls.", "generated_by": "figures-src/quantum-information/generate-tilted-ising-membrane-transfer.py", "generator_sha256": "d90323d6960decdcbffcde73780191c5a8ee5b77545101cf3a8b65ac346f9408", "csv_sha256": "4e4f081e1e414f2cfb0cd63268bbd5685c5757c94dc518980a7915adf0fc435b", "randomness": "none", "seeds": [], "entropy_logarithm": "natural", "content_units": { "entropy": "nat", "time": "J^-1", "energy_density": "J/site", "lattice_spacing": 1.0, "hbar": 1.0 } }, "model": { "hamiltonian": "H=sum_{j=1}^{L-1} Z_j Z_{j+1}+h sum_j Z_j-1.05 sum_j X_j", "boundary_condition": "open", "J_ZZ": 1.0, "transverse_field_g": -1.05, "chaotic_longitudinal_field_h": 0.5, "integrable_longitudinal_field_h": 0.0, "equilibrium_entropy_density_nats_per_site": 0.6931471805599453, "equilibrium_entropy_density_basis": "The Hamiltonian is traceless and the initial energy density is exactly zero, so the matched Gibbs state has beta=0 and s_eq=ln 2." }, "initial_state": { "state": "tensor_product_of_plus_y_on_every_site", "single_site_state": "(|0>+i|1>)/sqrt(2)", "exact_initial_energy_density": 0.0, "matched_energy_density_across_chaotic_and_integrable_runs": true }, "data_split": { "training_observable": "von Neumann entropy across [0,x)", "training_cuts_x": [ 6, 7, 8, 9, 10 ], "training_time_min_J_inverse": 1.2, "training_time_max_J_inverse": 3.0, "training_time_step_J_inverse": 0.2, "training_time_sample_count": 10, "held_out_observable": "von Neumann entropy of the centered eight-site interval", "held_out_interval_sites_L16_zero_based": [ 4, 5, 6, 7, 8, 9, 10, 11 ], "held_out_interval_sites_L18_zero_based": [ 5, 6, 7, 8, 9, 10, 11, 12 ], "held_out_geometry_used_in_fit": false }, "numerics": { "method": "second-order Strang splitting", "split": "exp(-i dt H_Z/2) exp(-i dt H_X) exp(-i dt H_Z/2)", "state_representation": "dense complex amplitude vector", "entropy_method": "singular values of the full-state subsystem coefficient matrix", "schmidt_probability_cutoff": 1e-14, "renormalize_probabilities_after_cutoff": true, "evolution_status": "direct dense-state second-order Strang evolution at the stated time step, not exact continuous-time evolution", "runs": [ { "label": "primary_chaotic_L16_dt002", "length": 16, "longitudinal_field": 0.5, "time_step_J_inverse": 0.02, "time_max_J_inverse": 3.2, "output_time_step_J_inverse": 0.2, "record_count": 17 }, { "label": "primary_integrable_L16_dt002", "length": 16, "longitudinal_field": 0.0, "time_step_J_inverse": 0.02, "time_max_J_inverse": 3.2, "output_time_step_J_inverse": 0.2, "record_count": 17 }, { "label": "control_chaotic_L16_dt001", "length": 16, "longitudinal_field": 0.5, "time_step_J_inverse": 0.01, "time_max_J_inverse": 3.2, "output_time_step_J_inverse": 0.2, "record_count": 17 }, { "label": "control_chaotic_L18_dt002", "length": 18, "longitudinal_field": 0.5, "time_step_J_inverse": 0.02, "time_max_J_inverse": 3.2, "output_time_step_J_inverse": 0.2, "record_count": 17 } ] }, "fit": { "model": "S_cut(t)=c+r t", "identified_membrane_datum": "E(0)=r/s_eq", "primary": { "time_min_J_inverse": 1.2, "time_max_J_inverse": 3.0, "sample_count": 10, "intercept_nats_per_boundary": -0.2801385577475653, "rate_nats_per_J_inverse_per_boundary": 0.7312563218172019, "E_at_zero_slope": 1.054979869104381, "rmse_nats": 0.02185841258232268, "maximum_absolute_residual_nats": 0.035375606083345446 }, "fit_window_envelope": { "lower_time_values_J_inverse": [ 1.0, 1.2, 1.4 ], "upper_time_values_J_inverse": [ 2.8, 3.0, 3.2 ], "window_count": 9, "fits": [ { "time_min_J_inverse": 1.0, "time_max_J_inverse": 2.8, "sample_count": 10, "intercept_nats_per_boundary": -0.262374392414158, "rate_nats_per_J_inverse_per_boundary": 0.7212363308815113, "E_at_zero_slope": 1.040524077871708, "rmse_nats": 0.020063352637312515, "maximum_absolute_residual_nats": 0.03414193773401075 }, { "time_min_J_inverse": 1.0, "time_max_J_inverse": 3.0, "sample_count": 11, "intercept_nats_per_boundary": -0.274942018238656, "rate_nats_per_J_inverse_per_boundary": 0.7290910970218228, "E_at_zero_slope": 1.051856110029678, "rmse_nats": 0.020975713716889836, "maximum_absolute_residual_nats": 0.034141937734011196 }, { "time_min_J_inverse": 1.0, "time_max_J_inverse": 3.2, "sample_count": 12, "intercept_nats_per_boundary": -0.2778582377714872, "rate_nats_per_J_inverse_per_boundary": 0.7308408287415216, "E_at_zero_slope": 1.0543804393045735, "rmse_nats": 0.020203465028847352, "maximum_absolute_residual_nats": 0.03402528895269796 }, { "time_min_J_inverse": 1.2, "time_max_J_inverse": 2.8, "sample_count": 9, "intercept_nats_per_boundary": -0.26405816185488773, "rate_nats_per_J_inverse_per_boundary": 0.721979170340657, "E_at_zero_slope": 1.041595768675594, "rmse_nats": 0.02113587066373021, "maximum_absolute_residual_nats": 0.03364671142791398 }, { "time_min_J_inverse": 1.2, "time_max_J_inverse": 3.0, "sample_count": 10, "intercept_nats_per_boundary": -0.2801385577475653, "rate_nats_per_J_inverse_per_boundary": 0.7312563218172019, "E_at_zero_slope": 1.054979869104381, "rmse_nats": 0.02185841258232268, "maximum_absolute_residual_nats": 0.035375606083345446 }, { "time_min_J_inverse": 1.2, "time_max_J_inverse": 3.2, "sample_count": 11, "intercept_nats_per_boundary": -0.2831520952909807, "rate_nats_per_J_inverse_per_boundary": 0.732930509341322, "E_at_zero_slope": 1.0573952111429474, "rmse_nats": 0.020921716288932822, "maximum_absolute_residual_nats": 0.03638011859781676 }, { "time_min_J_inverse": 1.4, "time_max_J_inverse": 2.8, "sample_count": 8, "intercept_nats_per_boundary": -0.30209290180803944, "rate_nats_per_J_inverse_per_boundary": 0.7382797731777222, "E_at_zero_slope": 1.0651125675521287, "rmse_nats": 0.01779238321043461, "maximum_absolute_residual_nats": 0.02670768740893581 }, { "time_min_J_inverse": 1.4, "time_max_J_inverse": 3.0, "sample_count": 9, "intercept_nats_per_boundary": -0.3164968195554485, "rate_nats_per_J_inverse_per_boundary": 0.7459961576852623, "E_at_zero_slope": 1.076244957214749, "rmse_nats": 0.017844979703975177, "maximum_absolute_residual_nats": 0.030308666845788812 }, { "time_min_J_inverse": 1.4, "time_max_J_inverse": 3.2, "sample_count": 10, "intercept_nats_per_boundary": -0.31468153140909166, "rate_nats_per_J_inverse_per_boundary": 0.745057215540595, "E_at_zero_slope": 1.074890350038956, "rmse_nats": 0.016952132297757334, "maximum_absolute_residual_nats": 0.029807897701966013 } ], "rate_minimum_nats_per_J_inverse_per_boundary": 0.7212363308815113, "rate_maximum_nats_per_J_inverse_per_boundary": 0.7459961576852623, "E_at_zero_slope_minimum": 1.040524077871708, "E_at_zero_slope_maximum": 1.076244957214749, "interpretation": "deterministic fit-window envelope, not a statistical confidence interval" } }, "held_out_geometry": { "length": 8, "prediction": "clip(2(c+r t),0,8 ln 2)", "prediction_uses_frozen_primary_fit": true, "comparison_time_min_J_inverse": 1.2, "comparison_time_max_J_inverse": 3.0, "metrics": { "sample_count": 10, "rmse_nats": 0.04351272607624914, "mean_absolute_error_nats": 0.03648481404687505, "maximum_absolute_error_nats": 0.0705983249232105, "bias_direct_minus_prediction_nats": 0.0021613078331520043 } }, "adversary": { "kind": "matched-energy integrable no-refit transfer", "integrable_parameter_change": "h: 0.5 -> 0.0", "fit_changed": false, "equilibrium_entropy_density_changed": false, "comparison_time_min_J_inverse": 1.2, "comparison_time_max_J_inverse": 3.0, "metrics": { "sample_count": 10, "rmse_nats": 0.7080023001707247, "mean_absolute_error_nats": 0.5916324967005165, "maximum_absolute_error_nats": 1.1877247952317282, "bias_direct_minus_prediction_nats": -0.5832609834110201 } }, "prehydrodynamic_control": { "time_J_inverse": 0.4, "direct_chaotic_interval_l8_nats": 0.615710095207903, "frozen_prediction_nats": 0.024727941958630928, "residual_direct_minus_prediction_nats": 0.5909821532492721, "interpretation": "same-model prehydrodynamic no-refit failure" }, "convergence": { "maximum_training_cut_translation_spread_nats": 0.00022397485234759706, "maximum_dt002_minus_dt001_cut_x8_difference_nats": 0.0001314037114314992, "maximum_dt002_minus_dt001_interval_l8_difference_nats": 0.0002026262870329365, "maximum_L16_minus_L18_central_cut_difference_nats": 3.181804140384159e-05, "maximum_L16_minus_L18_interval_l8_difference_nats": 0.040157409192782545, "run_diagnostics": [ { "label": "primary_chaotic_L16_dt002", "maximum_norm_error": 3.241851231905457e-14, "maximum_absolute_energy_density_drift": 0.000369426718334882, "maximum_complement_mismatch_nats": 5.551115123125783e-16, "complement_checks": [ { "time_J_inverse": 0.4, "absolute_mismatch_nats": 5.551115123125783e-16 }, { "time_J_inverse": 1.2, "absolute_mismatch_nats": 2.220446049250313e-16 }, { "time_J_inverse": 2.0, "absolute_mismatch_nats": 0.0 }, { "time_J_inverse": 3.2, "absolute_mismatch_nats": 0.0 } ] }, { "label": "primary_integrable_L16_dt002", "maximum_norm_error": 3.752553823233029e-14, "maximum_absolute_energy_density_drift": 0.0004034462247207958, "maximum_complement_mismatch_nats": 8.881784197001252e-16, "complement_checks": [ { "time_J_inverse": 0.4, "absolute_mismatch_nats": 3.3306690738754696e-16 }, { "time_J_inverse": 1.2, "absolute_mismatch_nats": 8.881784197001252e-16 }, { "time_J_inverse": 2.0, "absolute_mismatch_nats": 8.881784197001252e-16 }, { "time_J_inverse": 3.2, "absolute_mismatch_nats": 8.881784197001252e-16 } ] }, { "label": "control_chaotic_L16_dt001", "maximum_norm_error": 2.4580337765200966e-13, "maximum_absolute_energy_density_drift": 9.231381543433562e-05, "maximum_complement_mismatch_nats": 8.881784197001252e-16, "complement_checks": [ { "time_J_inverse": 0.4, "absolute_mismatch_nats": 0.0 }, { "time_J_inverse": 1.2, "absolute_mismatch_nats": 0.0 }, { "time_J_inverse": 2.0, "absolute_mismatch_nats": 4.440892098500626e-16 }, { "time_J_inverse": 3.2, "absolute_mismatch_nats": 8.881784197001252e-16 } ] }, { "label": "control_chaotic_L18_dt002", "maximum_norm_error": 3.730349362740526e-14, "maximum_absolute_energy_density_drift": 0.0003709939268102528, "maximum_complement_mismatch_nats": 8.881784197001252e-16, "complement_checks": [ { "time_J_inverse": 0.4, "absolute_mismatch_nats": 2.220446049250313e-16 }, { "time_J_inverse": 1.2, "absolute_mismatch_nats": 2.220446049250313e-16 }, { "time_J_inverse": 2.0, "absolute_mismatch_nats": 8.881784197001252e-16 }, { "time_J_inverse": 3.2, "absolute_mismatch_nats": 0.0 } ] } ] }, 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