TY - JOUR

T1 - Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems

AU - Kuwahara, Tomotaka

AU - Saito, Keiji

N1 - Funding Information:
The work of 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 (JP16H02211 and JP19H05603).
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/1/22

Y1 - 2021/1/22

N2 - In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as R-α, where R is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate α. In this regard, a crucial open challenge is to identify the optimal condition for α such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with α>D (D: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as α>D and the necessary scrambling time over a distance R is larger than t≳R[(2α-2D)/(2α-D+1)].

AB - In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as R-α, where R is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate α. In this regard, a crucial open challenge is to identify the optimal condition for α such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with α>D (D: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as α>D and the necessary scrambling time over a distance R is larger than t≳R[(2α-2D)/(2α-D+1)].

UR - http://www.scopus.com/inward/record.url?scp=85099778317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099778317&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.126.030604

DO - 10.1103/PhysRevLett.126.030604

M3 - Article

C2 - 33543944

AN - SCOPUS:85099778317

VL - 126

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 3

M1 - 030604

ER -