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  • Letter
  • Open Access

Unifying the Anderson transitions in Hermitian and non-Hermitian systems

Xunlong Luo1,*, Zhenyu Xiao2,†, Kohei Kawabata3,4,‡, Tomi Ohtsuki5,§, and Ryuichi Shindou2,∥

  • 1Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China
  • 2International Center for Quantum Materials, Peking University, Beijing 100871, China
  • 3Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 4Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
  • 5Physics Division, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan

  • *luoxunlong@pku.edu.cn
  • †wjkxzy@pku.edu.cn
  • ‡kohei.kawabata@princeton.edu
  • §ohtsuki@sophia.ac.jp
  • ∥rshindou@pku.edu.cn
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Phys. Rev. Research 4, L022035 – Published 11 May, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022035

Abstract

Non-Hermiticity enriches the tenfold 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 propose a correspondence of the universality classes of the ATs between Hermitian and non-Hermitian systems. We illustrate 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 of the correspondence 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†, CII†, and DIII in two and three dimensions. Estimated critical exponents are consistent with the proposed correspondence. According to the correspondence, some of the exponents also give useful information of the unknown critical exponents in Hermitian systems, paving a way to study the ATs of Hermitian systems by the corresponding non-Hermitian systems.

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Phys. Rev. Research 4, L022035– Published 11 May, 2022
  • Received 6 May 2021
  • Revised 8 April 2022
  • Accepted 20 April 2022
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