Disentangling transitions in topological order induced by boundary decoherence

Understand

We study the entanglement structure of topological orders subject to decoherence on the bipartition boundary.

• Focusing on the toric codes in $d$ space dimensions for $d=2,3,4$, we explore whether the boundary decoherence may be able to induce a disentangling transition, characterized by the destruction of mixed-state long-range entanglement across the bipartition, measured by topological entanglement negativity.
• A key insight of our approach is the connection between the negativity spectrum of the decohered mixed states and emergent symmetry-protected topological orders under certain symmetry-preserving perturbation localized on the bipartition boundary.
• This insight allows us to analytically derive the exact results of entanglement negativity without using a replica trick.