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

Simon Trebst; Philipp Werner; Matthias Troyer; Kirill Shtengel; Chetan Nayak

doi:10.1103/physrevlett.98.070602

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

Simon Trebst·Philipp Werner·Matthias Troyer·Kirill Shtengel·Chetan Nayak

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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.

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Simon Trebst, Philipp Werner, Matthias Troyer, Kirill Shtengel, Chetan Nayak. 2006-09-03. Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension. https://doi.org/10.1103/physrevlett.98.070602

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