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Published July 2020 | Published + Submitted
Journal Article Open

Hierarchy of Linear Light Cones with Long-Range Interactions

Abstract

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state |ψ⟩, O_x(t)O_y|ψ⟩≈O_yO_x(t)|ψ⟩ with arbitrarily small errors—so long as |x−y|≳vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/r^α. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state |ψ⟩ when α>3 (Lieb-Robinson light cone); for a typical state |ψ⟩ chosen uniformly at random from the Hilbert space when α>5/2 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

Additional Information

© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 11 February 2020; revised 1 May 2020; accepted 29 May 2020; published 13 July 2020. We thank Ana Maria Rey for useful discussions. M. C. T., A. Y. G., A. D., A. E., and A. V. G. acknowledge support by the DoE ASCR Quantum Testbed Pathfinder program (Grant No. DE-SC0019040), DoE ASCR FAR-QC (Grant No. DE-SC0020312), NSF Physics Frontier Center QC program, AFOSR Multidisciplinary University Research Initiative, AFOSR, ARO Multidisciplinary University Research Initiative, DoE BES Materials and Chemical Sciences Research for Quantum Information Science program (Grant No. DE-SC0019449), ARL CDQI, and NSF Physics Frontier Center at JQI. C.-F. C. is supported by the Millikan graduate fellowship at Caltech. A. Y. G. is supported by the NSF Graduate Research Fellowship Program under Grant No. DGE-1840340. A. E. also acknowledges funding from the DoD. Z.-X. G. is supported by the NSF RAISE-TAQS program under Grant No. CCF-1839232.

Attached Files

Published - PhysRevX.10.031009.pdf

Submitted - 2001.11509.pdf

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Additional details

Created:
August 19, 2023
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October 20, 2023