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.

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

References in corpus (6)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Local stabilizer codes in three dimensions without string logical operators
• Criticality, the area law, and the computational power of PEPS
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• On thermalization in Kitaev's 2D model
• Locality estimes for complex time evolution in 1D

Cited by in corpus (8)

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• 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