标题： 通过金属-绝缘体转变表征多体局域化交叉：从极化和量子度规中得到的局域化长度 显示英文标题

标题： Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric

摘要： 多体局域化（MBL）代表了一种独特的物理现象，为探索热化或更准确地说其失败提供了实验场所。 在这里，我们通过许多体量子度量（MBQM）在扭边参数空间中定义，并通过现代极化和绝缘体理论中定义的局域化参数，从几何上表征MBL区域。 首先，我们证明量子度量可以用于表征无序绝缘态，通过将这一理论框架应用于一维安德森绝缘体的激发态。 在那里，尽管在热力学极限下这些状态是无隙的，但在有限实现中观察到MBQM和局域化参数之间存在关系。 然后，我们考虑一个无序的一维玻色-哈伯德模型，并发现通过比较MBQM和局域化参数可以表征遍历-MBL交叉。 我们发现可以在MBL区域中提取一个自然的局域化长度，该长度表征波函数在实空间的扩展，并可以通过提取量子度量来测量。 我们的分析提供了对MBL区域的补充见解，重点在于其绝缘特性，并提供了一个在一系列绝缘相中定义一致的局域化长度。 显示英文摘要

摘要： Many body localization (MBL) represents a unique physical phenomenon, providing a testing ground for exploring thermalization, or more precisely its failure. Here we characterize the MBL regime geometrically by the many-body quantum metric (MBQM), defined in the parameter space of twist boundary, and the localization parameter as defined in the modern theory of polarization and insulators. First, we demonstrate that the quantum metric can be used to characterize disordered insulating states by applying this theoretical framework to excited states of the 1D Anderson insulator. There we observe that the MBQM and localization parameter are related in finite realizations despite the states being gapless in the thermodynamic limit. Then, we consider a disordered 1D Bose-Hubbard model and find that we can characterize the ergodic-MBL crossover by comparing the MBQM and localization parameter. We find that we can extract a natural localization length in the MBL regime that characterizes the real space spread of the wave function and can be measured by extracting the quantum metric. Our analysis provides complementary insight into the MBL regime focusing on its insulating properties and providing a localization length whose definition is consistent across a range of insulating phases.