Quantum phase transitions out of a Z2 x Z2 topological phase

Abstract

We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising interactions, using high-order series expansion and exact diagonalization. In a uniform magnetic field, we find 1st-order phase transitions in all field directions. In contrast, our results for the Ising interactions unveil that for strong enough Ising couplings, the Z2 x Z2 topological phase of color code breaks down to symmetry broken phases by 1st- or 2nd-order phase transitions.

10 pages, 11 figures

References in corpus (11)

• Topological Quantum Distillation
• Topological Order and Conformal Quantum Critical Points
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Adiabatic Preparation of Topological Order
• Phase diagram of the toric code model in a parallel magnetic field
• Breakdown of a perturbed Z_N topological phase
• Statistical Mechanical Models and Topological Color Codes
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Entanglement properties of topological color codes
• Persisting topological order via geometric frustration

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• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
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• A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems
• Analytical percolation theory for topological color codes under qubit loss
• A quantum phase transition from $Z_2\times Z_2$ to $Z_2$ topological order
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries