Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev Lett. 2019 Oct 18;123(16):160401. doi: 10.1103/PhysRevLett.123.160401.
Quantum chaotic interacting N-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales ∼logN. Here, we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-N limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing ℏ/τ, again given by τ∼logN. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasiperiodic recurrences indicating reversibility.
量子混沌相互作用的 N 粒子系统被认为在短（ Ehrenfest ）时间尺度 ∼logN 上表现出量子信息的快速和不可逆扩散。在这里，我们表明，在接近临界点时，某些多体系统表现出快速的初始混乱，随后在信息在 Hilbert 空间中的再入局部化和去局部化之间表现出振荡行为。我们考虑了具有吸引力接触相互作用的可积和不可积量子临界玻色子系统，它们在大 N 极限的相应多体相空间中表现出局部不稳定的动力学。后者的半经典量子化与模拟非常吻合地描述了多体相关性。值得注意的是，它预测了局部能级间距 ℏ/τ的渐近常数，同样由 τ∼logN 给出。这个独特的时间尺度控制了时间外相关函数的长时间行为，它们具有准周期性的递归，表明了可逆性。
