Critical behavior and collective modes at the superfluid transition in amorphous systems,Physical Review B

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Critical behavior and collective modes at the superfluid transition in amorphous systems
Physical Review B ( IF 3.2 ) Pub Date : 2024-07-16 , DOI: 10.1103/physrevb.110.024206
Pulloor Kuttanikkad Vishnu ₁ , Martin Puschmann ₂ , Rajesh Narayanan ₁ , Thomas Vojta ₂

Affiliation

We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map the two-dimensional Bose-Hubbard Hamiltonian defined on a random Voronoi-Delaunay lattice onto a (

2 + 1

)-dimensional layered classical XY model with correlated topological disorder. We study the resulting model by laying recourse to classical Monte Carlo simulations. We specifically focus on the scalar susceptibility of the order parameter to study the dynamics of the amplitude mode. To do so, we harness the maximum entropy method to perform the analytic continuation of the scalar susceptibility to real frequencies. Our analysis shows that the amplitude mode remains delocalized in the presence of such topological disorder, quite at odds with its behavior in generic disordered systems, where the randomness localizes the Higgs mode. Furthermore, we show that the critical behavior of the topologically disordered system is identical to that of its translationally invariant counterpart, consistent with a modified Harris criterion. This suggests that the localization of the collective excitations in the presence of disorder is tied to the critical behavior of the quantum phase transition rather than a simple Anderson-localization-type interference mechanism.

中文翻译：

非晶系统超流转变的临界行为和集体模式

我们研究了非晶系统（即受拓扑随机性影响的系统）中接近超流体-绝缘体量子相变的振幅（希格斯）模式的临界行为和动力学。特别是，我们将随机 Voronoi-Delaunay 晶格上定义的二维 Bose-Hubbard Hamiltonian 映射到具有相关拓扑无序的 (

2 + 1

) 维分层经典 XY 模型。我们通过经典的蒙特卡罗模拟来研究所得模型。我们特别关注阶次参数的标量敏感性来研究振幅模式的动力学。为此，我们利用最大熵方法来执行标量敏感性对实际频率的解析延拓。我们的分析表明，在存在这种拓扑无序的情况下，振幅模式仍然是离域的，这与它在一般无序系统中的行为非常不一致，在一般无序系统中，随机性使希格斯模式局域化。此外，我们表明拓扑无序系统的临界行为与其平移不变系统的临界行为相同，与修改后的哈里斯准则一致。这表明，在无序存在的情况下集体激发的局域化与量子相变的关键行为有关，而不是简单的安德森局域化型干涉机制。

更新日期：2024-07-16

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