Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos

Abstract

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 ${\mathbb{Z}}_4$ classification of fermion parity symmetry and antiunitary symmetry in the double Hilbert space, which contrasts with the ${\mathbb{Z}}_8$ 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.

36 pages, 21 figures, 10 tables

References in corpus (30)

• Classification of topological insulators and superconductors in three spatial dimensions
• Making Sense of Non-Hermitian Hamiltonians
• Anderson Transitions
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• An Open-System Quantum Simulator with Trapped Ions
• Quantum trajectories and open many-body quantum systems
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian topological phenomena: A review
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• PT-symmetric quantum Liouvillian dynamics
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Lindbladian dissipation of strongly-correlated quantum matter
• Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Many-body quantum chaos and emergence of Ginibre ensemble
• Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• Level statistics of real eigenvalues in non-Hermitian systems
• Probing quantum chaos in multipartite systems
• Supermetal-insulator transition in a non-Hermitian network model
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

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• Quantum Dynamics in Krylov Space: Methods and Applications
• On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
• Universality in driven open quantum matter
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Many-Body Open Quantum Systems
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Field theory of non-Hermitian disordered systems
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Edge modes and symmetry-protected topological states in open quantum systems
• Quantum Chaos and Coherence: Random Parametric Quantum Channels
• Breakdown of the Quantum Distinction of Regular and Chaotic Classical Dynamics in Dissipative Systems
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• An exactly solvable dissipative spin liquid
• Multifractality of many-body non-Hermitian skin effect
• Decoherence rate in random Lindblad dynamics
• Decomposing the Spectral Form Factor
• Chaotic and quantum dynamics in driven-dissipative bosonic chains
• Universal hard-edge statistics of non-Hermitian random matrices
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Higher-order gap ratios of singular values in open quantum systems
• Topology of Discrete Quantum Feedback Control
• Letting the tiger out of its cage: bosonic coding without concatenation
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Transient and steady-state chaos in dissipative quantum systems
• Integrability versus chaos in the steady state of many-body open quantum systems
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Symmetry classes of classical stochastic processes
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Correspondence principle, dissipation, and Ginibre ensemble
• Stable time rondeau crystals in dissipative many-body systems
• Symmetry and Topology of Monitored Quantum Dynamics
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Symmetry induced enhancement in finite-time thermodynamic trade-off relations
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Chaos in Time: A Dissipative Continuous Quasi Time Crystals
• Open-system dynamics in local Lindbladians with chaotic spectra
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains
• Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$