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Diagnosing quantum many-body chaos in non-Hermitian quantum spin chain via Krylov complexity

Yijia Zhou1,*, Wei Xia2, Lin Li3, and Weibin Li4

  • 1Shanghai Qi Zhi Institute, Shanghai 200232, China
  • 2Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China
  • 3National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 4School of Physics and Astronomy, and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom

  • *Contact author: zhouyijia@sqz.ac.cn
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Phys. Rev. Research 7, 033281 – Published 24 September, 2025

DOI: https://doi.org/10.1103/fw62-j2n9

Abstract

We investigate the phase transitions from chaotic to nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder, which can be realized with a Rydberg atom array setting. As the disorder strength increases, the emergence of nonchaotic dynamics is qualitatively captured through the suppressed growth of Krylov complexity and quantitatively identified through the reciprocity breaking of Krylov space. We further find that the localization in Krylov space generates another transition in the weak disorder regime, suggesting a weak ergodicity breaking. Our results closely align with conventional methods, such as the entanglement entropy and complex level spacing statistics, and pave the way to explore non-Hermitian phase transitions using Krylov complexity and associated metrics.

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Phys. Rev. Research 7, 033281– Published 24 September, 2025
  • Received 9 February 2025
  • Accepted 8 September 2025
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