Generalized multifractality at metal-insulator transitions and in metallic phases of two-dimensional disordered systems
Generalized multifractality at metal-insulator transitions and in metallic phases of two-dimensional disordered systems
复制标题
二维无序系统金属-绝缘体转变和金属相的广义多重分形
作者：
Jonas F. Karcher;I. Gruzberg;A. Mirlin
研究了对称类AII、D和DIII的无序系统中特征态涨落和相关的广义多重分形。考虑了金属相和安德森局域化转变。利用非线性西格玛模型方法，构造了纯尺度特征函数观测值。通过适当的微观模型的数值模拟验证了该结构，并得出了相应指数的数值。在金属相中，数值得到的指数满足Weyl对称关系和广义抛物线性（与二次卡西米尔算子的特征值成比例）。同时，在金属-绝缘体跃迁的临界点处，广义抛物线性被强烈破坏，表明局部共形不变性被破坏。此外，在D类和DIII类中，即使Weyl对称也会在金属-绝缘体过渡的临界点处被破坏。最后一个特征与这些对称类中的sigma模型流形的特性有关：它们由两个不相交的分量组成。与这些额外自由度相关的畴壁对于确保安德森定位至关重要，同时也会导致违反Weyl对称性。
We study generalized multifractality characterizing fluctuations and correlations of eigenstates in disordered systems of symmetry classes AII, D, and DIII. Both metallic phases and Andersonlocalization transitions are considered. By using the non-linear sigma-model approach, we construct pure-scaling eigenfunction observables. The construction is verified by numerical simulations of appropriate microscopic models, which also yield numerical values of the corresponding exponents. In the metallic phases, the numerically obtained exponents satisfy Weyl symmetry relations as well as generalized parabolicity (proportionality to eigenvalues of the quadratic Casimir operator). At the same time, the generalized parabolicity is strongly violated at critical points of metal-insulator transitions, signalling violation of local conformal invariance. Moreover, in classes D and DIII, even the Weyl symmetry breaks down at critical points of metal-insulator transitions. This last feature is related with a peculiarity of the sigma-model manifolds in these symmetry classes: they consist of two disjoint components. Domain walls associated with these additional degrees of freedom are crucial for ensuring Anderson localization and, at the same time, lead to the violation of the Weyl symmetry.
影响因子：
3.7
作者：
Rodriguez, Alberto;Vasquez, Louella J.;Roemer, Rudolf A.
通讯作者：
Roemer, Rudolf A.
影响因子：
2.4
作者：
Heinzner, P;Huckleberry, A;Zirnbauer, MR
通讯作者：
Zirnbauer, MR