Boundary and Symmetry Breaking in a Deformed Toric Code

This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary operators, allowing us to show that the transition is accompanied by the breaking of one higher-form symmetry. Using a holographic $(1+1)$-dimensional boundary Hamiltonian, we extract an effective central charge and find a pronounced suppression near $\beta_c$, followed by its restoration at strong coupling, indicating sensitivity to bulk criticality rather than topological order.