Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos

Kohei Kawabata, Anish Kulkarni, Jiachen Li, Tokiro Numasawa, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review


We develop a theory of symmetry in open quantum systems. Using the operator-state mapping, we characterize symmetry of Liouvillian superoperators for the open quantum dynamics by symmetry of operators in the double Hilbert space and apply the 38-fold internal-symmetry classification of non-Hermitian operators. We find rich symmetry classification due to the interplay between symmetry in the corresponding closed quantum systems and symmetry inherent in the construction of the Liouvillian superoperators. As an illustrative example of open quantum bosonic systems, we study symmetry classes of dissipative quantum spin models. For open quantum fermionic systems, we develop the Z4 classification of fermion parity symmetry and antiunitary symmetry in the double Hilbert space, which contrasts with the Z8 classification in closed quantum systems. We also develop the symmetry classification of open quantum fermionic many-body systems - a dissipative generalization of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation. We establish the periodic tables of the SYK Lindbladians and elucidate the difference from the SYK Hamiltonians. Furthermore, from extensive numerical calculations, we study its complex-spectral statistics and demonstrate dissipative quantum chaos enriched by symmetry.

Original languageAmerican English
Article number030328
JournalPRX Quantum
Issue number3
StatePublished - Jul 2023

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • General Computer Science
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics
  • Electrical and Electronic Engineering

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