Thermalization in Kitaev's quantum double models via Tensor Network techniques
Quantum Physics
2023-11-29 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2107.01628,
title = {Thermalization in Kitaev's quantum double models via Tensor Network techniques},
author = {Angelo Lucia and David Pérez-García and Antonio Pérez-Hernández},
journal= {arXiv preprint arXiv:2107.01628},
year = {2023}
}
Comments
84 pages. The paper has been restructured significantly. Some proofs have been corrected and simplified, and additional details have been provided throughout the paper