Breakdown of a Topological Phase: Quantum Phase Transition in a Loop Gas Model with Tension

2006/09/03 by Simon Trebst, Philipp Werner, Matthias Troyer +2 · 7 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el #hep-lat #quant-ph

paper · pdf · doi:10.1103/physrevlett.98.070602

published as Phys. Rev. Lett. 98, 070602 (2007). · 5 pages, 7 figures

arxiv created 2006/09/03 · openalex publication_date 2007/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 relate our results to error rates for topological quantum computations.

Citations

• Phase Diagram and Critical Exponents of a Dissipative Ising Spin Chain in a Transverse Magnetic Field
• Quantum tunnelling in a dissipative system
• Topologically protected quantum bits using Josephson junction arrays
• String-net condensation: A physical mechanism for topological phases
• Dynamics of the dissipative two-state system
• Fault-tolerant quantum computation by anyons

Cited by

• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order
• Breakdown of a perturbed \boldsymbol\mathbbmZ_N topological phase
• Anyonic braiding in optical lattices
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Topological Phase Transitions in the Golden String-Net Model
• Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids