Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
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DOI：
10.1103/physrevb.82.035309
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发表时间：
2009-11
影响因子：
3.7
通讯作者：
H. Obuse;A. Subramaniam;A. Furusaki;I. Gruzberg;A. Ludwig
中科院分区：
文献类型：
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作者：
H. Obuse;A. Subramaniam;A. Furusaki;I. Gruzberg;A. Ludwig
我们概括了二维（Anderson）定位-离域转变处典型波函数幅度标度的多重分形指数 � 0 与准一维（Q1D）几何中典型定位长度的相应临界有限尺寸标度（FSS）振幅 c 之间的普遍关系：（i）当在 Q1D 样本（条带几何）的横向上施加开放边界条件时，我们表明相应的临界 FSS 振幅普遍与边界相关沿直边界（表面）的典型波函数振幅的多重分形指数。 （ii）我们进一步提出将这些普遍关系推广到那些状态密度在转变时消失的对称类。 （iii）我们验证了以下四种类型的二维安德森跃迁的广义关系（方程（6）和（7））：（a）自旋轨道（辛）对称类中的金属到（普通绝缘体）跃迁，（b）同样属于自旋轨道（辛）类的金属到（Z2拓扑绝缘体）跃迁，（c）整数量子霍尔平台跃迁，以及(d)自旋量子霍尔平台跃迁。 PACS 编号：73.20.Fz、05.45.Df、72.15.Rn
We generalize universal relations between the multifractal exponent � 0 for the scaling of the typical wave function magnitude at a (Anderson) localization-delocalization transition in two dimensions and the corresponding critical finite size scaling (FSS) amplitudec of the typical localization length in quasi-one-dimensional (Q1D) geometry: (i) When open boundary conditions are imposed in the transverse direction of Q1D samples (strip geometry), we show that the corresponding critical FSS amplitudeo is universally related to the boundary multifractal exponents for the typical wave function amplitude along a straight boundary (surface). (ii) We further propose a generalization of these universal relations to those symmetry classes whose density of states vanishes at the transition. (iii) We verify our generalized relations (Eqs. (6) and (7)) numerically for the following four types of two-dimensional Anderson transitions: (a) the metal-to-(ordinary insulator) transition in the spin- orbit (symplectic) symmetry class, (b) the metal-to-(Z2 topological insulator) transition which is also in the spin-orbit (symplectic) class, (c) the integer quantum Hall plateau transition, and (d) the spin quantum Hall plateau transition. PACS numbers: 73.20.Fz, 05.45.Df, 72.15.Rn