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Real-time dynamics of one-dimensional and two-dimensional bosonic quantum matter deep in the many-body localized phase
Physical Review B ( IF 3.2 ) Pub Date : 2021-10-25 , DOI: 10.1103/physrevb.104.144205 Sun Woo Kim 1 , Giuseppe De Tomasi 2 , Markus Heyl 1
Physical Review B ( IF 3.2 ) Pub Date : 2021-10-25 , DOI: 10.1103/physrevb.104.144205 Sun Woo Kim 1 , Giuseppe De Tomasi 2 , Markus Heyl 1
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Recent experiments in quantum simulators have provided evidence for the many-body localized (MBL) phase in one-dimensional (1D) and two-dimensional (2D) bosonic quantum matter. The theoretical study of such a bosonic MBL phase, however, is a daunting task due to the unbounded nature of its Hilbert space. In this work, we introduce a method to compute the long-time real-time evolution of 1D and 2D bosonic systems in an MBL phase at strong disorder and weak interactions. We focus on local dynamical indicators that are able to distinguish an MBL phase from an Anderson localized one. In particular, we consider the temporal fluctuations of local observables, the spatiotemporal behavior of two-time correlators and out-of-time-correlators. We show that these few-body observables can be computed with a computational effort that depends only polynomially on the system size but is independent of the target time, by extending a recently proposed numerical method [G. De Tomasi, F. Pollmann, and M. Heyl, Phys. Rev. B 99, 241114(R) (2019)] to mixed states and bosons. Our method also allows us to surrogate our numerical study with analytical considerations of the time-dependent behavior of the studied quantities.
中文翻译：
多体局域相深处一维和二维玻色子量子物质的实时动力学
最近在量子模拟器中的实验为一维 (1D) 和二维 (2D) 玻色子量子物质中的多体局域化 (MBL) 相提供了证据。然而，由于其希尔伯特空间的无限性质，对这种玻色 MBL 相的理论研究是一项艰巨的任务。在这项工作中，我们引入了一种方法来计算强无序和弱相互作用下 MBL 阶段中一维和二维玻色子系统的长期实时演化。我们专注于能够区分 MBL 阶段和安德森本地化阶段的局部动态指标。特别是，我们考虑了局部可观测值的时间波动、二次相关器和超时相关器的时空行为。我们表明，通过扩展最近提出的数值方法 [G. De Tomasi、F. Pollmann 和 M. Heyl，物理。Rev. B 99 , 241114(R) (2019)] 到混合态和玻色子。我们的方法还允许我们通过对研究量的时间相关行为的分析考虑来替代我们的数值研究。
更新日期：2021-10-26
中文翻译：
多体局域相深处一维和二维玻色子量子物质的实时动力学
最近在量子模拟器中的实验为一维 (1D) 和二维 (2D) 玻色子量子物质中的多体局域化 (MBL) 相提供了证据。然而，由于其希尔伯特空间的无限性质，对这种玻色 MBL 相的理论研究是一项艰巨的任务。在这项工作中，我们引入了一种方法来计算强无序和弱相互作用下 MBL 阶段中一维和二维玻色子系统的长期实时演化。我们专注于能够区分 MBL 阶段和安德森本地化阶段的局部动态指标。特别是，我们考虑了局部可观测值的时间波动、二次相关器和超时相关器的时空行为。我们表明，通过扩展最近提出的数值方法 [G. De Tomasi、F. Pollmann 和 M. Heyl，物理。Rev. B 99 , 241114(R) (2019)] 到混合态和玻色子。我们的方法还允许我们通过对研究量的时间相关行为的分析考虑来替代我们的数值研究。
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