Quantum phase transition in the $Z_3$ Kitaev-Potts model

Abstract

The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low energy sector of the Kitaev-Potts model is mapped to the Potts model in the presence of transverse magnetic field. Our study relies on two high-order series expansion based on continuous unitary transformations in the limits of small- and large-Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the $Z_3$ Kitaev model breaks down to the Potts model through a first order phase transition. We capture the phase transition by analysis of the ground state energy, one-quasiparticle gap and geometric measure of entanglement.

12 pages, 10 figures, Accepted for publication in Physical Review B

References in corpus (13)

• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• The geometric measure of entanglement for symmetric states
• Adiabatic Preparation of Topological Order
• A statistical mechanics view on Kitaev's proposal for quantum memories
• Qudit surface codes and gauge theory with finite cyclic groups
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Probing topological order with Rényi entropy
• On the robustness of topological quantum codes: Ising perturbation
• The Kitaev-Ising model, Transition between topological and ferromagnetic order

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• A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems
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• The quantum (non-Abelian) Potts model and its exact solution