๏‚›GitHub๏„

๐ŸŸข XXZ1D/Energy/Infinite

Provisional v2 view โ€” RES not wired

Generated by docs/atlas/generate.jl โ€” 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 โ€” a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.

Assurance level: corroborated-at-p

Independently corroborated. See the cards below.

src claim

  • method bethe_ansatz, status exact, reliability high, refs: Hulthen1938 | YangYang1966
  • Closed form at ฮ” โˆˆ {-1, 0, 1}; Yang-Yang single integral via QuadGK for general -1 < ฮ” < 1; |ฮ”| > 1 (gapped) deferred.

Corroboration

regimemechanismindependencerefsfile
@fmlimiting_case๐ŸŸก assertedFM saturation: all-aligned state is exact GS, e0 = -J/4test/models/quantum/XXZ/test_XXZ1D.jl
@fmsecond_closed_form๐ŸŸข structuralXXZ FM point ฮ”=-1: aligned state exact, e0 = -J/4test/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@free_fermioned_finite_size๐ŸŸข structuralYang-Yang 1966 I: e0 = -J/pi for Delta=0 (free fermion)test/models/quantum/XXZ/test_XXZ1D.jl
@free_fermioned_finite_size๐ŸŸข structuralYang-Yang 1966 I: e0 = -J/pi for XX (Delta=0) free fermiontest/models/quantum/XXZ/test_xxz_xx_infinite.jl
@gaplessed_finite_size๐ŸŸข structuralYang-Yang 1966 II: e0 = -3J/8 at Delta=1/2 (gamma=pi/3)test/models/quantum/XXZ/test_XXZ1D.jl
@gaplessed_finite_size๐ŸŸข structuralIndependent OBC dense-ED ground-state energies at N=8,10,12 then 1/N-extrapolated (edge-defect leading correction); cross-checks the Yang-Yang single-integral closed form at ฮ” = 1/2test/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@gaplesslimiting_case๐ŸŸก assertedHeisenberg AF ฮ”โ†’1โป limit: e0 โ†’ 1/4 โˆ’ log 2 (des Cloizeaux-Pearson 1962)test/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@gaplesslimiting_case๐ŸŸก assertedFM ฮ”โ†’-1โบ limit: e0 โ†’ -J/4 (aligned saturated state, continuous from ฮ” = -1)test/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@gaplesslimiting_case๐ŸŸก assertedXX free-fermion limit: e0 = -J/ฯ€ at ฮ” = 0 (Lieb-Schultz-Mattis 1961); Yang-Yang continuous from ฮ” โ†’ 0โบtest/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@gaplesslimiting_case๐ŸŸก assertedXX free-fermion limit: e0 = -J/ฯ€ at ฮ” = 0; Yang-Yang continuous from ฮ” โ†’ 0โปtest/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@gaplesssecond_closed_form๐ŸŸข structuralYang-Yang 1966 II eq.(4.4): e0 = -3J/8 at ฮ” = 1/2 (ฮณ = ฯ€/3)test/verification/heisenberg_xxz/test_xxz_yang_yang.jl
@su2ed_finite_size๐ŸŸข structuralHulthen 1938: e0 = J(1/4 - log 2) at Delta=1test/models/quantum/XXZ/test_XXZ1D.jl

Test calls

The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):

verify(XXZ1D(; J = 1.0, ฮ” = -1.0), Energy(), Infinite(); route = :limiting_case, independent = -0.25, agree_within = 1.0e-14, refs = ["FM saturation: all-aligned state is exact GS, e0 = -J/4"])
verify(XXZ1D(; J = 1.0, ฮ” = -1.0), Energy(), Infinite(); route = :second_closed_form, independent = -0.25, agree_within = 1.0e-12, refs = ["XXZ FM point ฮ”=-1: aligned state exact, e0 = -J/4"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.0), Energy(), Infinite(); route = :ed_finite_size, independent = [xxz_e0_ed(1.0, 0.0, N) for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], at = ["N=$(N)" for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], agree_within = 0.05, refs = ["Yang-Yang 1966 I: e0 = -J/pi for Delta=0 (free fermion)"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.0), Energy(), Infinite(); route = :ed_finite_size, independent = [(dense_spectrum(chain_hamiltonian(2, N, kron(Sx, Sx) + kron(Sy, Sy))))[1] / (N - 1) for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], at = ["N=$(N)" for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], agree_within = 0.05, refs = ["Yang-Yang 1966 I: e0 = -J/pi for XX (Delta=0) free fermion"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.5), Energy(), Infinite(); route = :ed_finite_size, independent = [xxz_e0_ed(1.0, 0.5, N) for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], at = ["N=$(N)" for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], agree_within = 0.05, refs = ["Yang-Yang 1966 II: e0 = -3J/8 at Delta=1/2 (gamma=pi/3)"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.5), Energy(), Infinite(); route = :ed_finite_size, independent = intercept, agree_within = 0.005, at = ["Ns=$([8, 10, 12])"], refs = ["Independent OBC dense-ED ground-state energies at N=8,10,12 then 1/N-extrapolated (edge-defect leading correction); cross-checks the Yang-Yang single-integral closed form at ฮ” = 1/2"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.999), Energy(), Infinite(); route = :limiting_case, independent = 0.25 - log(2.0), agree_within = 0.001, at = ["ฮ”=0.999"], refs = ["Heisenberg AF ฮ”โ†’1โป limit: e0 โ†’ 1/4 โˆ’ log 2 (des Cloizeaux-Pearson 1962)"])
verify(XXZ1D(; J = 1.0, ฮ” = -0.999), Energy(), Infinite(); route = :limiting_case, independent = -0.25, agree_within = 0.001, at = ["ฮ”=-0.999"], refs = ["FM ฮ”โ†’-1โบ limit: e0 โ†’ -J/4 (aligned saturated state, continuous from ฮ” = -1)"])
verify(XXZ1D(; J = 1.0, ฮ” = 1.0e-6), Energy(), Infinite(); route = :limiting_case, independent = -1 / ฯ€, agree_within = 1.0e-5, at = ["ฮ”=1e-6"], refs = ["XX free-fermion limit: e0 = -J/ฯ€ at ฮ” = 0 (Lieb-Schultz-Mattis 1961); Yang-Yang continuous from ฮ” โ†’ 0โบ"])
verify(XXZ1D(; J = 1.0, ฮ” = -1.0e-6), Energy(), Infinite(); route = :limiting_case, independent = -1 / ฯ€, agree_within = 1.0e-5, at = ["ฮ”=-1e-6"], refs = ["XX free-fermion limit: e0 = -J/ฯ€ at ฮ” = 0; Yang-Yang continuous from ฮ” โ†’ 0โป"])
verify(XXZ1D(; J = 1.0, ฮ” = 0.5), Energy(), Infinite(); route = :second_closed_form, independent = -3 / 8, agree_within = 1.0e-10, refs = ["Yang-Yang 1966 II eq.(4.4): e0 = -3J/8 at ฮ” = 1/2 (ฮณ = ฯ€/3)"])
verify(XXZ1D(; J = 1.0, ฮ” = 1.0), Energy(), Infinite(); route = :ed_finite_size, independent = [xxz_e0_ed(1.0, 1.0, N) for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], at = ["N=$(N)" for N = verify_profile_Ns(; fast = (6, 8), full = (6, 8, 10, 12), nightly = (6, 8, 10, 12, 14))], agree_within = 0.05, refs = ["Hulthen 1938: e0 = J(1/4 - log 2) at Delta=1"])

Assurance (provisional)

  • level: corroborated-at-p ๐ŸŸข
  • cards: 12 ยท model ED-feasible
  • RES not wired โ€” measured residuals / confidence are not shown yet.

โ† Model: XXZ1D ยท Quantity: Energy ยท Atlas index