IndisputableMonolith.Physics.TopologicalPhaseTransitionFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Topological Phase Transition from J-Cost — Tier F Condensed Matter
   6
   7Topological phase transitions (Kosterlitz-Thouless, quantum Hall, topological insulator
   8transitions) are characterised by changes in topological invariants without
   9symmetry breaking. In RS terms, the topological sector is governed by
  10the recognition recognition winding number on the Brillouin zone.
  11
  12The KT transition temperature T_KT corresponds to J(r) crossing the
  13canonical band J(phi) ∈ (0.11, 0.13) for the vortex-antivortex
  14recognition ratio r = (bound pairs)/(unbound pairs).
  15
  16Five canonical topological phases (trivial, Z2 insulator, Z insulator,
  17Chern insulator, quantum Hall) = configDim D = 5.
  18
  19Lean status: 0 sorry, 0 axiom.
  20-/
  21
  22namespace IndisputableMonolith.Physics.TopologicalPhaseTransitionFromJCost
  23open Common.CanonicalJBand
  24
  25inductive TopologicalPhase where
  26  | trivial | Z2Insulator | ZInsulator | ChernInsulator | quantumHall
  27  deriving DecidableEq, Repr, BEq, Fintype
  28
  29theorem topologicalPhaseCount : Fintype.card TopologicalPhase = 5 := by decide
  30
  31structure TopologicalPhaseCert where
  32  five_phases : Fintype.card TopologicalPhase = 5
  33  transition_threshold : CanonicalCert
  34
  35noncomputable def topologicalPhaseCert : TopologicalPhaseCert where
  36  five_phases := topologicalPhaseCount
  37  transition_threshold := cert
  38
  39end IndisputableMonolith.Physics.TopologicalPhaseTransitionFromJCost
  40