Universality classes of the Anderson transition in the three-dimensional symmetry classes AIII, BDI, C, D, and CI
Universality classes of the Anderson transition in the three-dimensional symmetry classes AIII, BDI, C, D, and CI
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三维对称类 AIII、BDI、C、D 和 CI 中安德森转变的普遍性类
DOI：
10.1103/physrevb.104.014206
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
and R. Shindou
中科院分区：
文献类型：
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作者：
T. Wang;T. Ohtsuki;and R. Shindou
我们澄清普遍的临界性质的离域-本地化过渡的三维酉和正交类粒子孔和/或手征对称性（类AIII，BDI，D，C和CI）。我们首先介绍紧束缚模型的立方晶格，属于这五个非标准对称类，分别。与超导体的Bogoliubov-de Gennes哈密顿量不同，所有五种模型在干净极限的动量空间中都有有限面积的费米面。因此，安德森转变的标度理论保证了这些模型中在有限无序强度下的离域-局域化转变的存在。基于这一期望，我们进行了广泛的传输矩阵计算的零能量本征态的准一维几何结构的无序紧束缚模型的李雅普诺夫指数。在安德森转变点附近，关联长度以普适的临界指数发散。使用有限尺寸标度分析的本地化长度，我们确定的临界指数的过渡和标度函数的（归一化）本地化长度在三个非标准的酉对称类：，和。我们对C类的结果与经典网络模型[M. Ortuño，Phys. Rev. Lett. 102，070603（2009）PRLTA00031 -900710.1103/PhysRevLett.102.070603]。两个非标准正交类的临界指数被估计为和。CI类的结果与另一个格点模型的结果一致，而BDI类的指数与节Dirac环模型的结果不一致[X. Luo，Phys. Rev. B 101，020202（R）（2020）2469-995010.1103/PhysRevB.101.020202]。
We clarify universal critical properties of delocalization-localization transitions in three-dimensional unitary and orthogonal classes with particle-hole and/or chiral symmetries (classes AIII, BDI, D, C, and CI). We first introduce tight-binding models on cubic lattice that belong to these five nonstandard symmetry classes, respectively. Unlike the Bogoliubov-de Gennes Hamiltonian for superconductors, all the five models have finite areas of Fermi surfaces in the momentum space in the clean limit. Thereby, the scaling theory of the Anderson transition guarantees the presence of the delocalization-localization transitions at finite disorder strength in these models. Based on this expectation, we carry out extensive transfer matrix calculations of the Lyapunov exponents for zero-energy eigenstates of the disordered tight-binding models with quasi-one-dimensional geometry. Near the Anderson transition point, the correlation length diverges with a universal critical exponent. Using finite-size scaling analysis of the localization length, we determine the critical exponent of the transitions and scaling function of the (normalized) localization length in the three nonstandard unitary symmetry classes:,, and. Our result of the class C is consistent with a previous study of classical network model [M. Ortuño , Phys. Rev. Lett. 102, 070603 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.070603]. The critical exponents of the two nonstandard orthogonal classes are estimated asand. Our result of the class CI is consistent with another previous study of a lattice model, while the exponent of the class BDI is at variance with the previous evaluation of nodal Dirac ring model [X. Luo , Phys. Rev. B 101, 020202(R) (2020)2469-995010.1103/PhysRevB.101.020202].