Thermalization in Kitaev's quantum double models via tensor network techniques

Lucia, Angelo; Pérez-García, David; Pérez-Hernández, Antonio

doi:10.1017/fms.2023.98

Published November 28, 2023 | Version Published

Journal Article Open

Thermalization in Kitaev's quantum double models via tensor network techniques

1. California Institute of Technology
2. Institute of Mathematical Sciences
3. Complutense University of Madrid
4. National University of Distance Education

We show that every ergodic Davies generator associated to any 2D Kitaev's quantum double model has a nonvanishing 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.

Copyright and License

© The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acknowledgement

We are grateful to the anonymous referees who significantly contributed to improving the presentation of this article and the correction to certain sections. This research was supported by grants from Ministerio de Ciencia e Innovación, Agencia Española de Investigación, MCIN/AEI/10.13039/501100011033 (grants MTM2017-88385-P, PID2020-113523GB-I00, SEV-2015-0554, and CEX2019-000904-S), Comunidad de Madrid (grant QUITEMAD-CM, ref. S2018/TCS-4342), and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 648913). A. L. acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship and by grant RYC2019-026475-I funded by MCIN/AEI/10.13039/501100011033 and “ESF Investing in your future”. A. P. H. acknowledges support from the grants “Juan de la Cierva Formación” (FJC2018-036519-I) and of the Escuela Técnica Superior de Ingenieros Industriales (Universidad Nacional de Educación a Distancia) of Spain, projects 2023-ETSII-UNED-01 and 2021-MAT11.

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