T23 — Entanglement Entropy

Topological order in the deconfined phase

Objective

Compute Rényi entanglement entropies for the Z₂ gauge theory ground state to verify topological order with γ = log(2).

Status

🔴 Blocked on T20 (Z₂ LGT configurations)

Theory

For a bipartition A|B, the nth Rényi entropy:

\[ S_n(A) = \frac{1}{1-n} \log \text{Tr}(\rho_A^n) \]

Topological entanglement entropy:

\[ S(A) = \alpha |\partial A| - \gamma + \dots \]

For Z₂ deconfined phase: γ = log(2)

Method

• Replica trick or swap operator from T20 configurations
• Subregion shapes: cylinder, slab, sphere
• Extract γ from S(L) scaling

References

• Paper: Section 4.3