Out-of-time-order correlation at a quantum phase transition
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 cor...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/113591 |
| Summary: | 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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