TY - JOUR
T1 - Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain
AU - Das, Avijit
AU - Chakrabarty, Saurish
AU - Dhar, Abhishek
AU - Kundu, Anupam
AU - Huse, David A.
AU - Moessner, Roderich
AU - Ray, Samriddhi Sankar
AU - Bhattacharjee, Subhro
N1 - Funding Information:
The authors acknowledge A. Baecker, S. Banerjee, R. Basu, J. Bec, C. Dasgupta, D. Dhar, R. Govindarajan, M. Kastner, V. Khemani, J. Kurchan, S. Lepri, S. N. Majumdar, A. Nahum, A. Politi, A. Polkovnikov, S. Ramaswamy, and S. Sabhapandit for useful discussions. S. B. and R. M. acknowledge MPG for funding through the partner group of strongly correlated systems at ICTS. S. B. acknowledges MPIPKS for hospitality. A D. and A. K. acknowledge support of the Indo-French Centre for the promotion of advanced research (IFCPAR) under Project No. 5604-2. A. K., S. S. R., and S. B. acknowledge the support of SERB-DST (India) for project Grants No. ECR/2017/000634, No. ECR/2015/00036, and No. ECR/2017/000504 respectively. A. D. acknowledges support from Grant No. EDNHS ANR-14-CE25-0011 of the French National Research Agency. The numerical calculations were done on the cluster Mowgli and zero at the ICTS-TIFR.
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/7/10
Y1 - 2018/7/10
N2 - We find that the effects of a localized perturbation in a chaotic classical many-body system - the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.
AB - We find that the effects of a localized perturbation in a chaotic classical many-body system - the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.
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U2 - 10.1103/PhysRevLett.121.024101
DO - 10.1103/PhysRevLett.121.024101
M3 - Article
C2 - 30085710
AN - SCOPUS:85050141584
SN - 0031-9007
VL - 121
JO - Physical Review Letters
JF - Physical Review Letters
IS - 2
M1 - 024101
ER -