论文标题
卡利树上的肮脏玻色子：玻色 - 因斯坦凝结与超生性破裂
Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
论文作者
论文摘要
在大规模量子蒙特卡洛模拟的基础上，我们研究了在以场地为中心的Cayley树中随机潜力的硬核玻色子的零温度相图，其分支数量$ k = 2 $。为了遵循Bose-Einstein冷凝物（BEC）如何受到该疾病的影响，我们专注于零孔密度，探测量子相干性和一体密度密度矩阵（1BDM），其最大的特征值监测了偏置长距离的远程长度。我们进一步研究了其相关的本征态，该状态带来了有关该领先本本征的真实空间特性的有用信息。随着随机性的增加，我们发现该系统在远程有限的BEC状态之间在有限障碍强度上进行量子相变，并且在大规模上完全令人难以置信，而新的无序玻璃玻璃制度显示了相干分数的常规定位，而1BDM则在1BDM中表现出非繁琐的代数bec密度与非无性化的效率相同。这些特性的特性可以通过在Cayley树上的简单现象学描述来分析捕获，该描述提供了Bose玻璃制度的物理图片。
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.
