论文标题
无序的Aubry-André模型中的量子关键性
Quantum criticality in the disordered Aubry-André model
论文作者
论文摘要
在本文中，我们探讨了无序的Aubry-André（AA）模型中的量子关键。对于纯AA模型，众所周知，它通过调谐准碘电势的强度，将其主持一个临界点，将扩展相和局部绝缘体相分开。在这里，我们发掘了混乱强度$δ$在AA模型的临界点附近贡献一个独立的相关方向。我们的缩放分析表明，本地化长度$δ$缩放为$δ$作为$ξ\proptoΔ^{ - ν_δ} $，$ν_δ$是一个新的关键指数，估计为$ν_Δ\ oft0.46 $。对于纯AA模型和Anderson模型，该值与同行截然不同。此外，在准膜碘和无序电位跨越的关键区域中发现了丰富的关键现象。特别是，在扩展阶段，我们表明缩放理论满足了AA模型的临界区域与安德森本地化之间的重叠的结果满足混合缩放形式。
In this paper, we explore quantum criticality in the disordered Aubry-André (AA) model. For the pure AA model, it is well-known that it hosts a critical point separating an extended phase and a localized insulator phase by tuning the strength of the quasiperiodic potential. Here we unearth that the disorder strength $Δ$ contributes an independent relevant direction near the critical point of the AA model. Our scaling analyses show that the localization length $ξ$ scales with $Δ$ as $ξ\proptoΔ^{-ν_Δ}$ with $ν_Δ$ a new critical exponent, which is estimated to be $ν_Δ\approx0.46$. This value is remarkably different from the counterparts for both the pure AA model and the Anderson model. Moreover, rich critical phenomena are discovered in the critical region spanned by the quasiperiodic and the disordered potentials. In particular, in the extended phase side, we show that the scaling theory satisfy a hybrid scaling form as a result of the overlap between the critical regions of the AA model and the Anderson localization.
