论文标题
在Cayley树上随机横向场中的行进/非旅行相变和非邻向特性
Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
论文作者
论文摘要
我们研究有限的卡利树上的随机横向域模型。这使我们能够探讨其他重要无序量子系统中引起的关键问题，尤其是安德森过渡和卡利树上肮脏的玻色子问题，或者在此类系统中出现了非共性特性。我们在数值上研究了这一问题基于腔均值方法，并以最先进的有限尺寸缩放分析进行了补充。我们的数字基于与吸收壁存在的分支随机行走的行动波问题的类比，与分析结果非常吻合。研究了零温度的磁磁性铁磁过渡的临界特性和有限大小的校正，以实现恒定和代数消失的边界条件。在后来的情况下，我们揭示了一个政权，它让人联想到其他系统中观察到的非脱离定位阶段，从而在无序量子系统的背景下阐明了关键问题，例如安德森过渡，多体性定位或无限尺寸中的多体定位或无序的玻色子。
We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant and algebraically vanishing boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.
