{
  "slug": "2026-09-10-spinon-propagation",
  "domain_wall_model": {
    "projection_check": {
      "validation_chain_sites": 9,
      "maximum_projected_matrix_difference": 1.4432899320127035e-15,
      "omitted_exchange_actions": 24,
      "limits": "Checks PH_XXZP, after subtracting common Neel and two-wall Ising energy. Virtual excursions to zero/four-wall sectors and the dressed ground state are not simulated."
    },
    "dynamical_checks": [
      {
        "kappa": 0.0,
        "sites": 101,
        "basis_size": 1225,
        "norm_error": 1.9984014443252818e-15,
        "larger_chain_sites": 141,
        "maximum_mean_separation_difference": 5.364597654988756e-13,
        "maximum_outer_edge_probability": 1.2533918204534509e-09,
        "initial_separation": 2.0,
        "final_mean_separation": 26.040019104397654,
        "maximum_mean_separation": 26.040019104397654,
        "left_wall_integrated_Sz": 0.5,
        "right_wall_integrated_Sz": -0.5
      },
      {
        "kappa": 0.15,
        "sites": 101,
        "basis_size": 1225,
        "norm_error": 1.8318679906315083e-14,
        "larger_chain_sites": 141,
        "maximum_mean_separation_difference": 1.5987211554602254e-14,
        "maximum_outer_edge_probability": 1.5739459737800584e-17,
        "initial_separation": 2.0,
        "final_mean_separation": 5.873496750289171,
        "maximum_mean_separation": 9.293448682074455,
        "left_wall_integrated_Sz": 0.5,
        "right_wall_integrated_Sz": -0.5
      }
    ],
    "limits": "Effective strong-Ising-limit two-domain-wall sector, initial even-segment flip with DeltaSz=0. Each wall hops2sites with amplitudeJxy/2; diagonal confinement=kappa*(r-l). No additional wall creation/annihilation, dressed vacuum or full YbAlO3 spin Hamiltonian. Probability maps are quantum expectations, not individual particle tracks or neutron response functions."
  },
  "two_spinon_kinematics": {
    "J_meV": 0.21,
    "J_over_kB_K": 2.4369488055255677,
    "chain_spacing_nm": 0.36565000000000003,
    "maximum_velocity_nm_per_ps": 0.18324788979248605,
    "35_spacings_nm": 12.79775,
    "40K_over_exchange_scale": 16.41396811837143,
    "100K_over_exchange_scale": 41.03492029592857,
    "numeric_vs_analytic_boundary_max_error_meV": 1.1102230246251565e-16,
    "limits": "Zero-temperature isotropic two-spinon sector only. Boundaries derived from the spinon dispersion and allowed momentum partitions, not neutron spectral weights or a bound excluding every higher-spinon state. Different Hamiltonian limit from the wall demo. 35spacings merely converts the author's model/resolution-dependent reported length; no linewidth refit."
  },
  "QFI_logic": {
    "Hamiltonian": "H/J=S1.S2",
    "generator": "S1z-S2z; normalized QFI=FQ/N,N=2",
    "QFI_witness_threshold_temperature": 0.4773924714909116,
    "PPT_entanglement_threshold_temperature": 0.9102392266268373,
    "example_T0p7": {
      "T_over_J": 0.7,
      "QFI_per_spin": 0.5426157987702002,
      "partial_transpose_min_eigenvalue": -0.081749434917681,
      "negativity": 0.081749434917681
    },
    "limits": "Exact2spin thermal counterexample to treating a failed witness as proof of separability. Not a spinon model, not YbAlO3 and not an inference of its entanglement temperature. Eigenbasis QFI and partial transpose compared with independent closed forms."
  }
}