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

• URL: http://arxiv.org/abs/2107.01628v3
• Date: Tue, 28 Nov 2023 12:25:40 GMT
• Title: Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Authors: Angelo Lucia, David P\'erez-Garc\'ia, Antonio P\'erez-Hern\'andez
• Abstract summary: 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 rigorously validates the extended belief that those models are useless as self-correcting quantum memories.
• Score: 0.27309692684728604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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