Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Source preparation

Pure preparation and coherent diary loading › Source preparation · lines 558–580

Hawk02-E@1#eq:KM-prep

Choose a normalized simultaneous spin eigenvector

S_{a} ∣ B_{s} ⟩ = s_{a} ∣ B_{s} ⟩, s_{a} \in {- 1, 1},

with a declared total fermion parity. For $β > 0$ , define

Z_{s} (β) ∣ Ω_{S} ⟩ = ⟨ B_{s} ∣ e^{- β H_{S}} ∣ B_{s} ⟩, = Z_{s} (β)^{- 1/2} e^{- β H_{S} /2} ∣ B_{s} ⟩ .

This is the Euclidean-filtered preparation motivated by KourkoulouMaldacena. Its exact finite-realization properties used here are elementary.

Displayed formulas in this passage

Hawk02-E@1#eq:KM-prep · line 567
$Z_{s} (β) ∣ Ω_{S} ⟩ = ⟨ B_{s} ∣ e^{- β H_{S}} ∣ B_{s} ⟩, = Z_{s} (β)^{- 1/2} e^{- β H_{S} /2} ∣ B_{s} ⟩ .$
unlabeled · line 561
$S_{a} ∣ B_{s} ⟩ = s_{a} ∣ B_{s} ⟩, s_{a} \in {- 1, 1},$