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Out-of-time-ordered correlators in a quantum Ising chain

Lin, Cheng-Ju and Motrunich, Olexei I. (2018) Out-of-time-ordered correlators in a quantum Ising chain. Physical Review B, 97 (14). Art. no. 144304. ISSN 2469-9950. doi:10.1103/PhysRevB.97.144304.

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Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a “shell-like” structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t^(−1) power law at long time t. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a “ball-like” structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t^(−1/4) for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a “ball-like” structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Lin, Cheng-Ju0000-0001-7898-0211
Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2018 American Physical Society. (Received 19 January 2018; published 18 April 2018) The authors would like to thank D. Aason, D. Chowdhury, A. Kitaev, and C. White for useful discussions. This work was supported by NSF through Grant No. DMR-1619696 and also by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:14
Record Number:CaltechAUTHORS:20180418-093907947
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85941
Deposited By: George Porter
Deposited On:18 Apr 2018 18:25
Last Modified:15 Nov 2021 20:33

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