利用量子猝灭探测多体迁移率边缘
Detecting a many-body mobility edge with quantum quenches
摘要：
多体局域化（MBL）跃迁是一种涉及无序量子多体哈密顿量的高激发本征态的量子相变，其从“扩展/遍历”（表现出广泛的纠缠熵和波动）演化到“局域化”（表现出纠缠和波动的面积律标度）。MBL跃迁可以由给定光谱范围内的无序强度驱动，或者由固定无序下的能量密度驱动-如果系统具有多体迁移率边缘。在这里，我们建议探索后一种机制，通过使用“量子猝灭光谱”，即通过量子猝灭的可变宽度，准备在一个可控的光谱区域内的本征态的叠加系统的状态。研究数值链的相互作用的无自旋费米子在准周期的潜力，我们认为，这个系统有一个多体流动性的边缘，我们表明，它的存在转化为一个明确的动力学过渡的时间演化紧接着淬火的准周期的潜力的强度，以及在长时间的准稳态的标度特性的过渡。我们的研究结果提出了一个实用的方案，多体迁移率边缘的实验观察使用冷原子设置。
英文摘要：
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
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