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๐Ÿ”ต Hubbard1D/ChargeGap/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: coherent

An independent card exists and the value satisfies an internal invariant; no external value re-derives it yet.

src claim

  • method bethe_ansatz, status exact, reliability high, refs: LiebWu1968 | Essler2005
  • Lieb-Wu integral ฮ”_c = (16tยฒ/U) โˆซโ‚^โˆž โˆš(ฯ‰ยฒ-1)/sinh(2ฯ€tฯ‰/U) dฯ‰ at half filling.

Corroboration

regimemechanismindependencerefsfile
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆžtest/models/quantum/misc/test_hubbard1d.jl
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆžtest/models/quantum/misc/test_hubbard1d.jl
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆžtest/models/quantum/misc/test_hubbard1d.jl
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968: ฮ”c โ†’ 0 as U โ†’ 0 with exponential form ฮ”c โˆ exp(-2ฯ€ t / U)test/models/quantum/misc/test_hubbard1d.jl
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968: ฮ”c โ†’ 0 as U โ†’ 0 with exponential form ฮ”c โˆ exp(-2ฯ€ t / U)test/models/quantum/misc/test_hubbard1d.jl
@sweeplimiting_case๐ŸŸก assertedLieb-Wu 1968: ฮ”c โ†’ 0 as U โ†’ 0 with exponential form ฮ”c โˆ exp(-2ฯ€ t / U)test/models/quantum/misc/test_hubbard1d.jl

Test calls

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

verify(Hubbard1D(; 1.0 = 1.0, 16.0 = 16.0, ฮผ = 16.0 / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = (16.0 - 4 * 1.0) + (8 * 1.0 ^ 2 * log(2)) / 16.0, agree_within = 0.02, refs = ["Lieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆž"])
verify(Hubbard1D(; 1.0 = 1.0, 24.0 = 24.0, ฮผ = 24.0 / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = (24.0 - 4 * 1.0) + (8 * 1.0 ^ 2 * log(2)) / 24.0, agree_within = 0.02, refs = ["Lieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆž"])
verify(Hubbard1D(; 0.5 = 0.5, 12.0 = 12.0, ฮผ = 12.0 / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = (12.0 - 4 * 0.5) + (8 * 0.5 ^ 2 * log(2)) / 12.0, agree_within = 0.02, refs = ["Lieb-Wu 1968 / Essler et al. 2005 Eq. 6.A.66: ฮ”_c โ†’ U - 4t + 8tยฒln(2)/U as U โ†’ โˆž"])
verify(Hubbard1D(; 0.5 = 0.5, 0.3 * 0.5 = 0.3 * 0.5, ฮผ = (0.3 * 0.5) / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = 0.0, agree_within = 0.0001, refs = ["Lieb-Wu 1968: ฮ”_c โ†’ 0 as U โ†’ 0 with exponential form ฮ”_c โˆ exp(-2ฯ€ t / U)"])
verify(Hubbard1D(; 1.0 = 1.0, 0.3 * 1.0 = 0.3 * 1.0, ฮผ = (0.3 * 1.0) / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = 0.0, agree_within = 0.0001, refs = ["Lieb-Wu 1968: ฮ”_c โ†’ 0 as U โ†’ 0 with exponential form ฮ”_c โˆ exp(-2ฯ€ t / U)"])
verify(Hubbard1D(; 2.0 = 2.0, 0.3 * 2.0 = 0.3 * 2.0, ฮผ = (0.3 * 2.0) / 2), ChargeGap(), Infinite(); route = :limiting_case, independent = 0.0, agree_within = 0.0001, refs = ["Lieb-Wu 1968: ฮ”_c โ†’ 0 as U โ†’ 0 with exponential form ฮ”_c โˆ exp(-2ฯ€ t / U)"])

Assurance (provisional)

  • level: coherent ๐Ÿ”ต
  • cards: 6 ยท model ED-feasible
  • RES not wired โ€” measured residuals / confidence are not shown yet.

โ† Model: Hubbard1D ยท Quantity: ChargeGap ยท Atlas index