Roy Nilanjan, Sharma Auditya
Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India.
Department of Physics, Indian Institute of Science, Bangalore 560012, India.
J Phys Condens Matter. 2021 Jun 25;33(33). doi: 10.1088/1361-648X/ac06e9.
We investigate the nonequilibrium dynamics of entanglement entropy and out-of-time-order correlator (OTOC) of noninteracting fermions at half-filling starting from a product state to distinguish the delocalized, multifractal (in the limit of nearest neighbor hopping), localized and mixed phases hosted by the quasiperiodic Aubry-André-Harper (AAH) model in the presence of long-range hopping. For sufficiently long-range hopping strength a secondary logarithmic behavior in the entanglement entropy is found in the mixed phases whereas the primary behavior is a power-law the exponent of which is different in different phases. The saturation value of entanglement entropy in the delocalized, multifractal and mixed phases depends linearly on system size whereas in the localized phase (in the short-range regime) it is independent of system size. The early-time growth of OTOC shows very different power-law behaviors in the presence of nearest neighbor hopping and long-range hopping. The late time decay of OTOC leads to noticeably different power-law exponents in different phases. The spatial profile of OTOC and its system-size dependence also provide distinct features to distinguish phases. In the mixed phases the spatial profile of OTOC shows two different dependences on space for small and large distances respectively. Interestingly the spatial profile contains large fluctuations at the special locations related to the quasiperiodicity parameter in the presence of multifractal states.
我们研究了半填充时非相互作用费米子的纠缠熵和时间反演关联函数（OTOC）的非平衡动力学，从一个乘积态开始，以区分在存在长程跳跃的情况下，由准周期奥布里 - 安德烈 - 哈珀（AAH）模型所呈现的离域、多分形（在最近邻跳跃极限下）、局域和混合相。对于足够长程的跳跃强度，在混合相中发现纠缠熵存在二次对数行为，而主要行为是幂律，其指数在不同相中不同。离域、多分形和混合相中的纠缠熵饱和值线性依赖于系统大小，而在局域相（在短程区域）中它与系统大小无关。在存在最近邻跳跃和长程跳跃的情况下，OTOC的早期增长表现出非常不同的幂律行为。OTOC的后期衰减在不同相中导致明显不同的幂律指数。OTOC的空间分布及其对系统大小的依赖性也提供了区分相的独特特征。在混合相中，OTOC的空间分布分别在小距离和大距离上表现出对空间的两种不同依赖性。有趣的是，在存在多分形态的情况下，空间分布在与准周期参数相关的特殊位置包含大的涨落。
