Cayley树上的脏玻色子：玻色-爱因斯坦凝聚与遍历破缺
Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
摘要：
基于大规模量子蒙特卡罗模拟，我们研究了分支数为$K=2$的格点中心Cayley树上随机势中硬核玻色子的零温相图。为了研究无序对玻色-爱因斯坦凝聚体（BEC）的影响，我们着重研究了零动量密度，探讨了量子相干性，以及单体密度矩阵（1BDM），它的最大本征值控制着非对角长程序.我们进一步研究了它的相关本征态，这带来了有用的信息，这个领先的本征模的实空间特性。在增加随机性，我们发现，该系统经历了一个量子相变在有限的无序强度之间的长程有序BEC状态，完全遍历在大尺度上，和一个新的无序玻色玻璃制度，显示传统的本地化的相干分数，而1BDM显示一个非平凡的代数消失BEC密度一起在实空间中的非遍历占领。这些特殊的属性可以分析捕获的一个简单的现象描述的凯莱树提供了一个物理图片的玻色玻璃制度。
英文摘要：
Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number $K=2$. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a non-trivial algebraic vanishing BEC density together with a non-ergodic occupation in real-space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime.
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