Boundary and Symmetry Breaking in a Deformed Toric Code

TL;DR

This paper investigates a deformation of the toric code that causes a phase transition characterized by symmetry breaking, revealing insights into the interplay between topological order and boundary symmetries.

Contribution

It introduces a specific deformation of the Kitaev toric code and analyzes the resulting phase transition and symmetry breaking using boundary and holographic methods.

Findings

Phase transition involves breaking of a higher-form symmetry.

Effective central charge shows suppression near critical point.

Bulk criticality influences boundary symmetry behavior.

Abstract

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.