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

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

2006-09-03

arxiv.org/abs/cond-mat/0609048v1

Phys. Rev. Lett. 98, 070602 (2007).

Physics

Condensed Matter

Statistical Mechanics

5 pages, 7 figures

Scientific paper

10.1103/PhysRevLett.98.070602

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.

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