Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension

Abstract

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.

5 pages, 7 figures

References in corpus (2)

• Topological Order and Conformal Quantum Critical Points
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field

Cited by in corpus (5)

• Entanglement and topological entropy of the toric code at finite temperature
• Error Threshold for Color Codes and Random 3-Body Ising Models
• A quantum topological phase transition at the microscopic level
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Reduced fidelity in topological quantum phase transitions