TY - JOUR
T1 - Symmetry of Open Quantum Systems
T2 - Classification of Dissipative Quantum Chaos
AU - Kawabata, Kohei
AU - Kulkarni, Anish
AU - Li, Jiachen
AU - Numasawa, Tokiro
AU - Ryu, Shinsei
N1 - Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2023/7
Y1 - 2023/7
N2 - 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.
AB - 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.
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U2 - 10.1103/PRXQuantum.4.030328
DO - 10.1103/PRXQuantum.4.030328
M3 - Article
AN - SCOPUS:85172904910
SN - 2691-3399
VL - 4
JO - PRX Quantum
JF - PRX Quantum
IS - 3
M1 - 030328
ER -