Bardet, Ivan and Capel, Ángela and Lucia, Angelo and Pérez-García, David and Rouzé, Cambyse (2021) On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems. Journal of Mathematical Physics, 62 (6). Art. No. 061901. ISSN 0022-2488. doi:10.1063/1.5142186. https://resolver.caltech.edu/CaltechAUTHORS:20210623-143016235
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Abstract
The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.
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| Additional Information: | © 2021 Published under an exclusive license by AIP Publishing. Submitted: 10 December 2019; Accepted: 29 May 2021; Published Online: 16 June 2021. The authors would like to thank Nilanjana Datta for fruitful discussions and for her comments on an earlier version of the draft. I.B. was supported by French A.N.R. (Grant No. ANR-14-CE25-0003 “StoQ”). A.C. was partially supported by a La Caixa-Severo Ochoa grant (ICMAT Severo Ochoa Project No. SEV-2011-0087, MINECO) and the MCQST Distinguished PostDoc fellowship from the Munich Center for Quantum Science and Technology. A.C. and D.P.-G. acknowledge support from MINECO (Grant No. MTM2017-88385-P) and from Comunidad de Madrid (Grant Nos. QUITEMAD-CM and ref. P2018/TCS-4342). A.L. acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant No. PHY-1733907), from the BBVA Fundation, and from the Spanish Ramón y Cajal Programme (RYC2019-026475-I / AEI / 10.13039/501100011033). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 648913). C.R. acknowledges financial support from the TUM University Foundation Fellowship and by the DFG Cluster of Excellence 2111 (Munich Center for Quantum Science and Technology). Data Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study. | ||||||||||||||||||||||||||||||||||
| Group: | Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics | ||||||||||||||||||||||||||||||||||
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| Issue or Number: | 6 | ||||||||||||||||||||||||||||||||||
| DOI: | 10.1063/1.5142186 | ||||||||||||||||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20210623-143016235 | ||||||||||||||||||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210623-143016235 | ||||||||||||||||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||||||||||||||||
| ID Code: | 109545 | ||||||||||||||||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||||||||||||||||||||||
| Deposited On: | 23 Jun 2021 18:34 | ||||||||||||||||||||||||||||||||||
| Last Modified: | 23 Jun 2021 18:34 |
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