🟢 TFIM/Energy/OBC
Generated by docs/atlas/generate.jl — a pure VIEW over the *_registry.jl claims + the static test/INVENTORY.jsonl AST scan. No test is executed and no src is run; test/INVENTORY.jsonl is regenerated in-place (idempotently) from that static scan; fetch/@register untouched. Assurance labels are PROVISIONAL: residuals / confidence are not shown yet (RES not wired). Badges reflect the committed test AST, not the latest CI run — a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.
src claim
- method
bdg, statusexact, reliabilityhigh, refs: Pfeuty1970 - Total ⟨H⟩(β) via the BdG spectrum; ground state when no β kwarg.
Corroboration
| regime | mechanism | independence | refs | file |
|---|---|---|---|---|
@disordered | sum_rule | 🟡 asserted | Tr(σz σz) = Tr(σx) = 0 => ⟨H⟩_{β=0} = 0 | test/models/quantum/TFIM/test_TFIM_thermal.jl |
@ordered | sum_rule | 🟡 asserted | Tr(σz σz)=Tr(σx)=0 => per-site ⟨H⟩_{β=0}=0 across all BC | test/identities/test_cross_bc_scaling.jl |
@sweep | second_closed_form | 🟢 structural | J=0 decoupled spins: ε = -h tanh(βh) per site | test/identities/test_TFIM_limits_cross_model.jl |
@sweep | second_closed_form | 🟢 structural | J=0 decoupled spins: ε = -h tanh(βh) per site | test/identities/test_TFIM_limits_cross_model.jl |
@sweep | second_closed_form | 🟢 structural | J=0 decoupled spins: ε = -h tanh(βh) per site | test/identities/test_TFIM_limits_cross_model.jl |
@sweep | ed_finite_size | 🟢 structural | GS energy = min eigenvalue of buildtfim_dense | test/models/quantum/TFIM/test_TFIM_dynamics_verify.jl |
@sweep | ed_finite_size | 🟢 structural | GS energy = min eigenvalue of buildtfim_dense (black-box ED) | test/models/quantum/TFIM/test_TFIM_local.jl |
@sweep | ed_finite_size | 🟢 structural | Direct OBC dense ED via buildtfimdense + thermofrom_spectrum | test/models/quantum/TFIM/test_TFIM_thermal.jl |
@sweep | ed_finite_size | 🟢 structural | Direct OBC dense ED via buildtfimdense + thermofrom_spectrum | test/models/quantum/TFIM/test_TFIM_thermal.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | "ED black-box: -J σz⊗σz bonds + -h σx onsite, full spectrum, thermofrom_spectrum (E)" | test/models/quantum/TFIM/test_TFIM_thermo_OBC_ED_batch.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | ed_finite_size | 🟢 structural | Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | limiting_case | 🟡 asserted | Classical Ising limit h=0: E_0^OBC = -J(N-1) exact (independent of dense ED) | test/verification/tfim_ising/test_tfim_gap_closure.jl |
@sweep | limiting_case | 🟡 asserted | Strong-field PT² limit h ≫ J: E_0^OBC ≈ -hN - J²(N-1)/(4h) (Rayleigh-Schrödinger, | +⟩^N unperturbed g.s., bond perturbation V = -J Σ σᶻσᶻ) |
@sweep | limiting_case | 🟡 asserted | Strong-field PT² limit h ≫ J: E_0^OBC ≈ -hN - J²(N-1)/(4h) (Rayleigh-Schrödinger, | +⟩^N unperturbed g.s., bond perturbation V = -J Σ σᶻσᶻ) |
@sweep | ed_finite_size | 🟢 structural | Independent sparse-ED via buildtfimsparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12) | test/verification/universality/test_universality_cross_check.jl |
@sweep | ed_finite_size | 🟢 structural | Independent sparse-ED via buildtfimsparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12) | test/verification/universality/test_universality_cross_check.jl |
@sweep | ed_finite_size | 🟢 structural | Independent sparse-ED via buildtfimsparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12) | test/verification/universality/test_universality_cross_check.jl |
@sweep | ed_finite_size | 🟢 structural | Independent sparse-ED via buildtfimsparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12) | test/verification/universality/test_universality_cross_check.jl |
Test calls
The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):
verify(TFIM(; J = 1.0, h = 1.3), Energy(), OBC(6); route = :sum_rule, fetch_kw = (; beta = 0.0), independent = 0.0, agree_within = 1.0e-10, refs = ["Tr(σz σz) = Tr(σx) = 0 => ⟨H⟩_{β=0} = 0"])verify(TFIM(; J = 1.0, h = 0.5), Energy(:per_site), OBC(8); route = :sum_rule, fetch_kw = (; beta = 0.0), independent = 0.0, agree_within = 1.0e-9, refs = ["Tr(σz σz)=Tr(σx)=0 => per-site ⟨H⟩_{β=0}=0 across all BC"])verify(TFIM(; J = 0.0, 1.0 = 1.0), Energy(:per_site), OBC(6); route = :second_closed_form, fetch_kw = (; beta = 0.7), independent = -1.0 * tanh(0.7 * 1.0), agree_within = 1.0e-8, refs = ["J=0 decoupled spins: ε = -h tanh(βh) per site"])verify(TFIM(; J = 0.0, 0.5 = 0.5), Energy(:per_site), OBC(6); route = :second_closed_form, fetch_kw = (; beta = 1.5), independent = -0.5 * tanh(1.5 * 0.5), agree_within = 1.0e-8, refs = ["J=0 decoupled spins: ε = -h tanh(βh) per site"])verify(TFIM(; J = 0.0, 2.0 = 2.0), Energy(:per_site), OBC(6); route = :second_closed_form, fetch_kw = (; beta = 0.3), independent = -2.0 * tanh(0.3 * 2.0), agree_within = 1.0e-8, refs = ["J=0 decoupled spins: ε = -h tanh(βh) per site"])verify(TFIM(; 1.0 = 1.0, 1.3 = 1.3), Energy(), OBC(6); route = :ed_finite_size, fetch_kw = (; beta = Inf), independent = (dense_spectrum(_build_tfim_dense(6, 1.0, 1.3)))[1], agree_within = 1.0e-9, refs = ["GS energy = min eigenvalue of _build_tfim_dense"])verify(TFIM(; 1.0 = 1.0, 1.5 = 1.5), Energy(), OBC(6); route = :ed_finite_size, fetch_kw = (; beta = Inf), independent = (dense_spectrum(_build_tfim_dense(6, 1.0, 1.5)))[1], agree_within = 1.0e-9, refs = ["GS energy = min eigenvalue of _build_tfim_dense (black-box ED)"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 1.0 = 1.0), independent = E_ind, agree_within = 1.0e-8, refs = ["Direct OBC dense ED via _build_tfim_dense + thermo_from_spectrum"])verify(TFIM(; 1.0 = 1.0, 1.5 = 1.5), Energy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 0.7 = 0.7), independent = E_ind, agree_within = 1.0e-8, refs = ["Direct OBC dense ED via _build_tfim_dense + thermo_from_spectrum"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(4); route = :ed_finite_size, independent = ed_E, at = ["N=$(4)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(6); route = :ed_finite_size, independent = ed_E, at = ["N=$(6)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 0.5 = 0.5))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 2.0 = 2.0))verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(:per_site), OBC(8); route = :ed_finite_size, independent = ed_E, at = ["N=$(8)"], agree_within = 1.0e-9, refs = ["ED black-box: -J σ_z⊗σ_z bonds + -h σ_x onsite, full spectrum, thermo_from_spectrum (E)"], fetch_kw = (; 5.0 = 5.0))verify(TFIM(; 1.0 = 1.0, 0.0 = 0.0), Energy(), OBC(4); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1])), at = ["J=$(1.0)", "h=$(0.0)", "N=$(4)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(), OBC(4); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1])), at = ["J=$(1.0)", "h=$(0.5)", "N=$(4)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(), OBC(4); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1])), at = ["J=$(1.0)", "h=$(1.0)", "N=$(4)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(), OBC(4); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1])), at = ["J=$(1.0)", "h=$(2.0)", "N=$(4)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 0.5 = 0.5, 1.5 = 1.5), Energy(), OBC(4); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 4, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1])), at = ["J=$(0.5)", "h=$(1.5)", "N=$(4)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 0.0 = 0.0), Energy(), OBC(6); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1])), at = ["J=$(1.0)", "h=$(0.0)", "N=$(6)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(), OBC(6); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1])), at = ["J=$(1.0)", "h=$(0.5)", "N=$(6)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(), OBC(6); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1])), at = ["J=$(1.0)", "h=$(1.0)", "N=$(6)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(), OBC(6); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1])), at = ["J=$(1.0)", "h=$(2.0)", "N=$(6)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 0.5 = 0.5, 1.5 = 1.5), Energy(), OBC(6); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 6, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1])), at = ["J=$(0.5)", "h=$(1.5)", "N=$(6)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 0.0 = 0.0), Energy(), OBC(8); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 0.0)))))[1])), at = ["J=$(1.0)", "h=$(0.0)", "N=$(8)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), Energy(), OBC(8); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 0.5)))))[1])), at = ["J=$(1.0)", "h=$(0.5)", "N=$(8)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(), OBC(8); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 1.0)))))[1])), at = ["J=$(1.0)", "h=$(1.0)", "N=$(8)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(), OBC(8); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 1.0, 2.0)))))[1])), at = ["J=$(1.0)", "h=$(2.0)", "N=$(8)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 0.5 = 0.5, 1.5 = 1.5), Energy(), OBC(8); route = :ed_finite_size, independent = (sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1], agree_within = max(1.0e-12, 1.0e-10 * abs((sort(eigvals(Symmetric(build_tfim(build_lattice(Square, 8, 1; boundary = OpenAxis()), 0.5, 1.5)))))[1])), at = ["J=$(0.5)", "h=$(1.5)", "N=$(8)"], refs = ["Independent dense-ED of build_tfim Lattice2D OBC chain (eigvals of Symmetric H = -J Σ σᶻσᶻ − h Σ σˣ) — cross-checks BdG analytical Energy OBC"])verify(TFIM(; 1.0 = 1.0, h = 0.0), Energy(), OBC(6); route = :limiting_case, independent = -1.0 * (6 - 1), agree_within = 1.0e-12, at = ["J=$(1.0)", "h=0.0", "N=$(6)"], refs = ["Classical Ising limit h=0: E_0^OBC = -J(N-1) exact (independent of dense ED)"])verify(TFIM(; 1.0 = 1.0, h = 100.0), Energy(), OBC(6); route = :limiting_case, independent = -100.0 * 6 - (1.0 ^ 2 * (6 - 1)) / (4 * 100.0), agree_within = max(1.0e-12, 1.0e-9 * abs(-100.0 * 6 - (1.0 ^ 2 * (6 - 1)) / (4 * 100.0))), at = ["J=$(1.0)", "h=$(100.0)", "N=$(6)"], refs = ["Strong-field PT² limit h ≫ J: E_0^OBC ≈ -hN - J²(N-1)/(4h) (Rayleigh-Schrödinger, |+⟩^N unperturbed g.s., bond perturbation V = -J Σ σᶻσᶻ)"])verify(TFIM(; 1.0 = 1.0, h = 1000.0), Energy(), OBC(6); route = :limiting_case, independent = -1000.0 * 6 - (1.0 ^ 2 * (6 - 1)) / (4 * 1000.0), agree_within = max(1.0e-12, 1.0e-9 * abs(-1000.0 * 6 - (1.0 ^ 2 * (6 - 1)) / (4 * 1000.0))), at = ["J=$(1.0)", "h=$(1000.0)", "N=$(6)"], refs = ["Strong-field PT² limit h ≫ J: E_0^OBC ≈ -hN - J²(N-1)/(4h) (Rayleigh-Schrödinger, |+⟩^N unperturbed g.s., bond perturbation V = -J Σ σᶻσᶻ)"])verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(), OBC(14); route = :ed_finite_size, independent = vals[1], agree_within = max(1.0e-10, 1.0e-8 * abs(vals[1])), at = ["J=$(1.0)", "h=$(1.0)", "N=$(14)"], refs = ["Independent sparse-ED via build_tfim_sparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12)"])verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), Energy(), OBC(16); route = :ed_finite_size, independent = vals[1], agree_within = max(1.0e-10, 1.0e-8 * abs(vals[1])), at = ["J=$(1.0)", "h=$(1.0)", "N=$(16)"], refs = ["Independent sparse-ED via build_tfim_sparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12)"])verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(), OBC(14); route = :ed_finite_size, independent = vals[1], agree_within = max(1.0e-10, 1.0e-8 * abs(vals[1])), at = ["J=$(1.0)", "h=$(2.0)", "N=$(14)"], refs = ["Independent sparse-ED via build_tfim_sparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12)"])verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), Energy(), OBC(16); route = :ed_finite_size, independent = vals[1], agree_within = max(1.0e-10, 1.0e-8 * abs(vals[1])), at = ["J=$(1.0)", "h=$(2.0)", "N=$(16)"], refs = ["Independent sparse-ED via build_tfim_sparse (KrylovKit Lanczos, krylovdim=30, tol=1e-11) on the real-space 2^N basis — pushes the BdG cross-check past dense-ED reach (N ≤ 12)"])Assurance (provisional)
- level: corroborated-at-p 🟢
- cards: 58 · model ED-feasible
- RES not wired — measured residuals / confidence are not shown yet.