IndisputableMonolith.Physics.QuantumEntanglementEntropyAreaLaw

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Quantum Entanglement Entropy Area Law — Physics Depth
   6
   7Five canonical area-law regimes (= configDim D = 5):
   8  gapped ground state, critical 1+1 CFT, topological order,
   9  many-body localized, thermalizing.
  10
  11Each regime has a distinct entanglement-entropy scaling with subsystem
  12size.
  13
  14Lean status: 0 sorry, 0 axiom.
  15-/
  16
  17namespace IndisputableMonolith.Physics.QuantumEntanglementEntropyAreaLaw
  18
  19inductive EntanglementRegime where
  20  | gappedGroundState
  21  | critical1p1CFT
  22  | topologicalOrder
  23  | manyBodyLocalized
  24  | thermalizing
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem entanglementRegime_count :
  28    Fintype.card EntanglementRegime = 5 := by decide
  29
  30structure EntanglementAreaLawCert where
  31  five_regimes : Fintype.card EntanglementRegime = 5
  32
  33def entanglementAreaLawCert : EntanglementAreaLawCert where
  34  five_regimes := entanglementRegime_count
  35
  36end IndisputableMonolith.Physics.QuantumEntanglementEntropyAreaLaw
  37