Out-of-time-order correlation at a quantum phase transition
Author(s)
Zhang, Pengfei; Fan, Ruihua; Zhai, Hui; Shen, Huitao
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Motivated by the recent studies of out-of-time-order correlation functions and the holographic duality, we propose the quantum critical point conjecture, which is stated as: For a many-body quantum system with a quantum phase transition, the Lyapunov exponent extracted from the out-of-time-order correlators will exhibit a maximum around the quantum critical region. We first demonstrate that the Lyapunov exponent is well defined in the one-dimensional Bose-Hubbard model with the help of the out-of-time-order correlation–Rényi-entropy theorem. We then support the conjecture by numerically computing the out-of-time-order correlators. We also compute the butterfly velocity, and propose an experiment protocol of measuring this correlator without inverting the Hamiltonian.
Date issued
2017-08Department
Massachusetts Institute of Technology. Department of PhysicsJournal
Physical Review B
Publisher
American Physical Society
Citation
Shen, Huitao, et al. “Out-of-Time-Order Correlation at a Quantum Phase Transition.” Physical Review B, vol. 96, no. 5, Aug. 2017. © 2017 American Physical Society
Version: Final published version
ISSN
2469-9950
2469-9969