On the stability of topological phases on a lattice

Abstract

We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken.

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• A short proof of stability of topological order under local perturbations
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• Breakdown of a perturbed Z_N topological phase
• Renormalization group constructions of topological quantum liquids and beyond
• Local topological order inhibits thermal stability in 2D
• Quasi-Topological Phases of Matter and Topological Protection
• Stability of local quantum dissipative systems
• Dynamics at and near conformal quantum critical points
• Perturbative analysis of topological entanglement entropy from conditional independence
• Stability of topologically invariant order parameters at finite temperature
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Rapid mixing and stability of quantum dissipative systems
• Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime
• Local convertibility of the ground state of the perturbed Toric code
• Josephson Coupled Moore-Read States
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$
• Fibonacci topological order from quantum nets
• Thermalization of Topological Entropy after a Quantum Quench
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Perturbative stability and error correction thresholds of quantum codes
• Self-correction in Wegner's 3D Ising lattice gauge theory
• Lieb-Robinson Bound at Finite Temperature
• Stability of ground state degeneracy to long-range interactions
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• A dynamical Toric Code model with fusion and de-fusion
• Toric code-like models from the parameter space of $3D$ lattice gauge theories
• Effect of slowly decaying long-range interactions on topological qubits
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• The geometry of the Hermitian matrix space and the Schrieffer--Wolff transformation