Thermalization in Kitaev's quantum double models via Tensor Network techniques

Abstract

We show that the Davies generator associated to any 2D Kitaev's quantum double model has a non-vanishing spectral gap in the thermodynamic limit. This validates rigorously the extended belief that those models are useless as self-correcting quantum memories, even in the non-abelian case. The proof uses recent ideas and results regarding the characterization of the spectral gap for parent Hamiltonians associated to Projected Entangled Pair States in terms of a bulk-boundary correspondence.

arXiv comment84 pages. The paper has been restructured significantly. Some proofs have been corrected and simplified, and additional details have been provided throughout the paper

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Cited by in corpus (8)

• Towards a classification of mixed-state topological orders in two dimensions
• Rapid thermalization of spin chain commuting Hamiltonians
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise
• On the critical finite-size gap scaling for frustration-free Hamiltonians
• Bounds on Autonomous Quantum Error Correction
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains