Unifying the Anderson transitions in Hermitian and non-Hermitian systems
Unifying the Anderson transitions in Hermitian and non-Hermitian systems
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DOI：
10.1103/physrevresearch.4.l022035
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发表时间：
2021-05
影响因子：
4.2
通讯作者：
Xunlong Luo;Zhenyu Xiao;K. Kawabata;T. Ohtsuki;Ryuichi Shindou
中科院分区：
文献类型：
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作者：
Xunlong Luo;Zhenyu Xiao;K. Kawabata;T. Ohtsuki;Ryuichi Shindou
非厄米性使Altland-Zirnbauer对称性从10重扩展到38重，其中安德森跃迁的临界行为近年来得到了广泛的研究。在这里，我们建立了厄米特和非厄米特系统之间的AT的普适性类的对应关系。我们证明了非厄米特系统的长度尺度的临界指数与相应的厄米特系统的临界指数具有额外的手征对称性。一个显着的结果是超普遍性，即，在某些不同对称类的非厄米特系统中，AT具有相同的临界指数。除了已知的临界指数之间的比较非厄米特系统和厄米特对应的，我们得到的临界指数在对称类AI，AII，AII$^{\dagger}$，CII$^{\dagger}$，和DIII在二维和三维。我们精确的临界指数不仅证实了对应关系，而且预测了厄米特系统中未知的临界指数，为用相应的非厄米特系统研究厄米特系统的AT铺平了道路.
Non-Hermiticity enriches the 10-fold Altland-Zirnbauer symmetry class into the 38-fold symmetry class, where critical behavior of the Anderson transitions (ATs) has been extensively studied recently. Here, we establish a correspondence of the universality classes of the ATs between Hermitian and non-Hermitian systems. We demonstrate that the critical exponents of the length scale in non-Hermitian systems coincide with the critical exponents in the corresponding Hermitian systems with additional chiral symmetry. A remarkable consequence is superuniversality, i.e., the ATs in some different symmetry classes of non-Hermitian systems are characterized by the same critical exponent. In addition to the comparisons between the known critical exponents for non-Hermitian systems and their Hermitian counterparts, we obtain the critical exponents in symmetry classes AI, AII, AII$^{\dagger}$, CII$^{\dagger}$, and DIII in two and three dimensions. Our precise critical exponents not only confirm the correspondence, but also predict the unknown critical exponents in Hermitian systems, paving a way to study the ATs of Hermitian systems by the corresponding non-Hermitian systems.