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113591 |
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|a Zhang, Pengfei
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|a Massachusetts Institute of Technology. Department of Physics
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|a Shen, Huitao
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|a Fan, Ruihua
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|a Zhai, Hui
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|a Shen, Huitao
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|a Out-of-time-order correlation at a quantum phase transition
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|b American Physical Society,
|c 2018-02-12T18:48:12Z.
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|u http://hdl.handle.net/1721.1/113591
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|a 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.
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|a National Natural Science Foundation (China) (Grant 11325418)
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|a Tsinghua University (Beijing, China). Initiative Scientific Research Program
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|a China. Ministry of Science and Technology (Grant 2016YFA0301600)
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|t Physical Review B
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