Disordered non-Hermitian systems and Anderson transitions have received significant attention in recent studies. Before investigating non-Hermitian systems, we will review the application of random matrix theory, and Anderson transitions in closed quantum systems. Subsequently, we will demonstrate that the non-Hermitian random matrix theory can describe the complex spectra of non-integrable systems [1], wherein symmetry plays a pivotal role. Furthermore, we establish a correspondence between of Anderson transitions in non-Hermitian and Hermitian Hamiltonians [2]. It not only enables the reuse of existing knowledge but also inspires the exploration of Hermitian Anderson transitions. As an example, a non-Hermitian system without reciprocity can be mapped to a Hermitian counterpart featuring a weak topological index, which exhibits a “quasi-localized” phase and a new universality class of Anderson transitions [3].

Reference:
[1] Z. Xiao et al., Phys. Rev. Research 4, 043196 (2022).
[2] X. Luo et al., Phys. Rev. Research 4, L022035 (2022).
[3] Z. Xiao et al., arXiv:2211.09999 (to appear in Phys. Rev. Lett.).

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