用Wegner流动方程研究一维定域转捩
Localization transition in one dimension using Wegner flow equations
摘要：
流动方程法是由Wegner提出的一种研究一维相互作用系统的方法。在这里，我们将这种方法应用到一个无序的一维模型与幂律衰减跳跃。该模型提出了一个作为衰减指数$α$的函数的过渡。我们推导出流方程，和单粒子运营商的演变。流动方程揭示了$α<1/2$的状态的离域性质。另外，在$α>1/2$体系中，我们提出了一个强键的重整化群结构，它是基于对三位团簇的迭代，在这里我们微扰地求解了流动方程。这种重整化群方法允许我们探测临界点$\left(α=1\right)$。这种方法正确地再现了临界水平间距统计，和分形维数的本征函数。
英文摘要：
The flow equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent $α$. We derive the flow equations, and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for $α<1/2$. Additionally, in the regime, $α>1/2$, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point $\left(α=1\right)$. This method correctly reproduces the critical level-spacing statistics, and the fractal dimensionality of the eigenfunctions.
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