论文标题
Aubry-André模型的量子保真度和指数正交性灾难
Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe
论文作者
论文摘要
我们通过计算Fermi液体的基础状态之间的重叠$ f $来考虑（扩展的）Aubry-André（AA） - 模型中的正交性灾难，因为该准晶体模型和具有附加潜在杂物的同一系统之一，因为该系统的函数是具有含义的大小的功能。最近，在量子关键阶段中发现了典型的保真度$ f _ {\ rm typ} $，以$ f \ sim \ exp（-c c l^{zη}）$ \ cite {kettemann2016}的形式呈指数衰减。对于关键的AA模型$η= 1/2 $是多重强度相关性的力量，而$ z $由于状态密度的分形结构而导致的动态指数，该密度在数值上被认为是$ z \ gg 1 $。然而，令人惊讶的是，我们发现在关键阶段，富达衰落的忠诚度具有较弱的单一站点杂质。即使发现它较小，并且腐烂速度比金属阶段快，但它并不能像预期的那样呈指数型。但是，在绝缘体阶段中，我们发现了指数的AOC，我们给出了统计解释，该机制与金属中的AOC有很大不同，在金属中，它是与连续状态的耦合，从而产生了限制忠诚度的功率定律。通过重新审查分析推导，我们确定了由于波函数之间的杂质潜力和多点相关性而导致的非扰动校正，可能是由于在临界阶段不存在指数AOC的原因。但是，对于扩展的杂质，我们发现在AA模型的量子临界点以及扩展AA模型的移动性边缘处的指数AOC的指示，并提出了该发现的解释。
We consider the orthogonality catastrophe in the (extended) Aubry-André (AA)-Model, by calculating the overlap $F$ between the ground state of the Fermi liquid in that quasi-crystalline model and the one of the same system with an added potential impurity, as function of the size of that impurity. Recently, the typical fidelity $F_{\rm typ}$ was found in quantum critical phases to decay exponentially with system size $L$ as $F \sim \exp(-c L^{z η})$\cite{Kettemann2016} as found in an analytical derivation due to critical correlations. For the critical AA model $η= 1/2$ is the power of multifractal intensity correlations, and $z$ the dynamical exponent due to the fractal structure of the density of states which is numerically found to be $z \gg 1$. Surprisingly, however, we find for a weak single site impurity that the fidelity decays with a power law, in the critical phase. Even though it is found to be smaller and decays faster than in the metallic phase, it does not decay exponentially as predicted. We find an exponential AOC however in the insulator phase for which we give a statistical explanation, a mechanism which is profoundly different from the AOC in metals, where it is the coupling to a continuum of states which yields there the power law suppression of the fidelity. By reexamination of the analytical derivation we identify nonperturbative corrections due to the impurity potential and multipoint correlations among wave functions as possible causes for the absence of the exponential AOC in the critical phase. For an extended impurity, however, we find indications of an exponential AOC at the quantum critical point of the AA model and at the mobility edge of the extended AA model and suggest an explanation for this finding.
