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Published December 2021 | Submitted + Published
Journal Article Open

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


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.

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.

Attached Files

Published - PhysRevA.104.062420.pdf

Submitted - 2105.09960.pdf


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August 20, 2023
October 23, 2023