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arXiv 1302.5839cond-mat.stat-mechcond-mat.dis-nn
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$-N$大极限下无序量子相变的数值方法

Numerical method for disordered quantum phase transitions in the large$-N$ limit

David Nozadze, Thomas Vojta

摘要:

我们发展了一种有效的数值方法来研究具有$\mathcal{O}(N)$序参量对称性的无序系统在大$-N$极限下的量子临界行为。它是基于大$-N$鞍点方程的迭代解,结合一种快速算法来反演所产生的大稀疏随机矩阵。作为一个例子,我们考虑了无序纳米线中超导体-金属的量子相变。我们研究了量子相变附近各种可观测量的行为。我们的结果与最近的重整化群预言一致,即,该跃迁由无限随机临界点控制,并伴有量子格里菲斯奇点。我们的方法是高效的,因为每次迭代的数值工作量与系统大小成线性关系。这使我们能够研究更大的系统,多达1024个网站,比以前的方法。我们还讨论了更高的维度和其他系统的概括,包括在无序金属的巡回反铁磁过渡。

英文摘要:

We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point equations combined with a fast algorithm for inverting the arising large sparse random matrices. As an example, we consider the superconductor-metal quantum phase transition in disordered nanowires. We study the behavior of various observables near the quantum phase transition. Our results agree with recent renormalization group predictions, i.e., the transition is governed by an infinite-randomness critical point, accompanied by quantum Griffiths singularities. Our method is highly efficient because the numerical effort for each iteration scales linearly with the system size. This allows us to study larger systems, with up to 1024 sites, than previous methods. We also discuss generalizations to higher dimensions and other systems including the itinerant antiferomagnetic transitions in disordered metals.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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