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Optimal Frobenius light cone in spin chains with power-law interactions

Chen, Chi-Fang and Lucas, Andrew (2021) Optimal Frobenius light cone in spin chains with power-law interactions. Physical Review A, 104 (6). Art. No. 062420. ISSN 2469-9926. doi:10.1103/physreva.104.062420. https://resolver.caltech.edu/CaltechAUTHORS:20211213-518520000

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Abstract

In many-body quantum systems with spatially local interactions, quantum information propagates with a finite velocity, reminiscent of the “light cone” of relativity. In systems with long-range interactions which decay with distance r as 1/r^α, however, there are multiple light cones which control different information theoretic tasks. We show an optimal (up to logarithms) “Frobenius light cone” obeying t ∼ r^(min(α−1,1)) for α > 1 in one-dimensional power-law interacting systems with finite local dimension: this controls, among other physical properties, the butterfly velocity characterizing many-body chaos and operator growth. We construct an explicit random Hamiltonian protocol that saturates the bound and settles the optimal Frobenius light cone in one dimension. We partially extend our constraints on the Frobenius light cone to a several operator p-norms, and show that Lieb-Robinson bounds can be saturated in at most an exponentially small e^(−Ω(r)) fraction of the many-body Hilbert space.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.104.062420DOIArticle
https://arxiv.org/abs/2105.09960arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Chi-Fang0000-0001-5589-7896
Additional Information:© 2021 American Physical Society. (Received 28 May 2021; revised 17 October 2021; accepted 26 November 2021; published 13 December 2021) We thank M. Tran and A. Gorshkov for helpful discussions and for collaboration on related work. A.L. was partially supported by a Research Fellowship from the Alfred P. Sloan Foundation, and by the Air Force Office of Scientific Research under Grant No. FA9550-21-1-0195.
Group:Infrared Processing and Analysis Center (IPAC)
Funders:
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-21-1-0195
Issue or Number:6
DOI:10.1103/physreva.104.062420
Record Number:CaltechAUTHORS:20211213-518520000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211213-518520000
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112376
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:13 Dec 2021 22:09
Last Modified:13 Dec 2021 22:09

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