T21 — CZX PEPS Ground State

Tensor network verification of SPT order

Objective

Construct the CZX plaquette state as a PEPS and verify its properties: area-law entanglement, spectral gap, and topological entanglement entropy.

Status

🔴 Blocked on T22 (spin foam amplitudes)

Theory

The CZX plaquette state (Eq. 64/65):

\[ |\psi\rangle = \prod_p CZ_p \cdot X_p |+\rangle^{\otimes N} \]

Claim: This is a short-range entangled state with Z₂ topological order.

Verification Criteria

1. Area-law entanglement: S(A) ∝ |∂A|
2. Spectral gap: Δ > 0
3. Topological entropy: γ = log(2)

References

• Paper: Section 5.2, Eqs. (64-65)