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New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains

Damanik, David and Lemm, Marius and Lukic, Milivoje and Yessen, William (2014) New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains. Physical Review Letters, 113 (12). Art. No. 127202. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20141209-150746627

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Abstract

We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone |x|≤v|t|, we obtain |x|≤v|t|α for some 0<α<1. We can characterize the allowed values of α exactly as those exceeding the upper transport exponent α+u of a one-body Schrödinger operator. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. We also discuss anomalous LR bounds with power-law tails for a random dimer field.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevLett.113.127202DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.127202PublisherArticle
http://arxiv.org/abs/1408.1796arXivDiscussion Paper
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Alternate Title:New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains
Additional Information:© 2014 American Physical Society. Received 13 August 2014; published 18 September 2014. D. Damanik was supported in part by NSF Grant No. DMS–1067988, M. Lukic was supported in part by NSF Grant No. DMS–1301582, and W. Yessen was supported by NSF Grant No. DMS–1304287. The authors wish to thank a referee for raising some interesting questions.
Funders:
Funding AgencyGrant Number
NSFDMS-1067988
NSFDMS-1301582
NSFDMS-1304287
Issue or Number:12
Classification Code:PACS: 75.10.Pq, 03.65.Ud, 05.50.+q, 05.60.Gg
Record Number:CaltechAUTHORS:20141209-150746627
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141209-150746627
Official Citation:New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains David Damanik, Marius Lemm, Milivoje Lukic, and William Yessen Phys. Rev. Lett. 113, 127202 (2014) – Published 18 September 2014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52515
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Dec 2014 23:51
Last Modified:09 Mar 2020 13:18

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