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Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions

Tomotaka Kuwahara and Keiji Saito
Phys. Rev. X 10, 031010 – Published 13 July 2020
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Abstract

In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as Rα with distance R. We prove the existence of the linear light cone for α>2D+1 (D, the spatial dimension), where we obtain the Lieb-Robinson bound as [Oi(t),Oj]t2D+1(Rv¯t)α with v¯=O(1) for two arbitrary operators Oi and Oj separated by a distance R. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for α<2D+1. In the regime of α>2D+1, our result characterizes the best general constraints on the information spreading.

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  • Received 25 March 2020
  • Revised 18 June 2020
  • Accepted 19 June 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031010

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

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A Speed Test for Ripples in a Quantum System

Published 13 July 2020

Settling a theoretical debate, three studies show that there is a maximum speed at which a physical effect can travel through systems of long-range-interacting particles.

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Authors & Affiliations

Tomotaka Kuwahara*

  • Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP), 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan and Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN 2-1, Hirosawa, Wako, Saitama 351-0198, Japan

Keiji Saito

  • Department of Physics, Keio University, Yokohama 223-8522, Japan

  • *tomotaka.kuwahara@riken.jp
  • saitoh@rk.phys.keio.ac.jp

Popular Summary

The speed of light puts a fundamental limit on the rate at which information can propagate, but such limits may also exist in nonrelativistic quantum systems. Understanding these limitations is critical to applications such as quantum computing and quantum optics. To that end, we mathematically investigate the nature of such limits in quantum systems dominated by long-range interactions.

Quantum systems with short-range interactions have a well-known upper limit to the speed at which information can propagate. This speed is known as the Lieb-Robinson velocity, and its exact value depends on the details of the system. However, beyond short-range interactions, the situation becomes highly elusive.

For long-range interactions described by a power law, information easily propagates to an arbitrarily distant point. This leads to an impression that there is no well-defined nonrelativistic limit for information transfer, and yet such a limit has been observed in some systems, depending on the exponent in the power law. We set out to determine what is the critical exponent for establishing such a limit and find that it is a function of the system’s spatial dimensions. Above the critical exponent, the speed of the quantum information is finite, while below it, the speed limit can be broken.

Our work reveals one of the most essential principles in quantum many-body dynamics with long-range interactions such as atomic, molecular, and optical dynamics.

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See Also

Hierarchy of Linear Light Cones with Long-Range Interactions

Minh C. Tran, Chi-Fang Chen, Adam Ehrenberg, Andrew Y. Guo, Abhinav Deshpande, Yifan Hong, Zhe-Xuan Gong, Alexey V. Gorshkov, and Andrew Lucas
Phys. Rev. X 10, 031009 (2020)

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Vol. 10, Iss. 3 — July - September 2020

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