TY - JOUR

T1 - Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions

AU - Kuwahara, Tomotaka

AU - Saito, Keiji

N1 - Funding Information:
T. K. was supported by the RIKEN Center for AIP and JSPS KAKENHI Grant No. 18K13475. K. S. was supported by JSPS Grants-in-Aid for Scientific Research (Grants No. JP16H02211, No. JP19H05791, and No. JP19H05603).
Publisher Copyright:
© 2020 authors.

PY - 2020/9

Y1 - 2020/9

N2 - 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 R-α 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(R-v¯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.

AB - 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 R-α 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(R-v¯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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U2 - 10.1103/PhysRevX.10.031010

DO - 10.1103/PhysRevX.10.031010

M3 - Article

AN - SCOPUS:85092728736

SN - 2160-3308

VL - 10

JO - Physical Review X

JF - Physical Review X

IS - 3

M1 - 031010

ER -