Scrambling dynamics and many-body chaos in a random dipolar spin model
| Autor: | Keles, Ahmet, Zhao, Erhai, Liu, W. Vincent |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 99, 053620 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.99.053620 |
| Popis: | Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. We map out the phase diagram of this model by computing the energy level statistics, spectral form factor, and out-of-time-order correlation (OTOC) functions. We find a broad regime of many-body chaos where the energy levels obey Wigner-Dyson statistics and the OTOC shows distinctive behaviors at different times: Its early-time dynamics is characterized by an exponential growth, while the approach to its saturated value at late times obeys a power law. The temperature scaling of the Lyapunov exponent $\lambda_L$ shows that while it is well below the conjectured bound $2\pi T$ at high temperatures, $\lambda_L$ approaches the bound at low temperatures and for large number of spins. Comment: 7 pages, 8 figures with updated references |
| Databáze: | arXiv |
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