Lindbladian dynamics of the Sachdev-Ye-Kitaev model

Abstract

We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large $N$, where $N$ is the number of Majorana fermion operators, and also in the limit of large $N$ and $M$, where $M$ is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite $N$, we also study the distribution of the eigenvalues of the SYK Lindbladians.

9 pages, 6 figures

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Cited by in corpus (37)

• Operator growth and Krylov construction in dissipative open quantum systems
• Operator growth in open quantum systems: lessons from the dissipative SYK
• Quantum Dynamics in Krylov Space: Methods and Applications
• On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Dynamical quantum phase transitions in SYK Lindbladians
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• The operator growth hypothesis in open quantum systems
• Field theory of non-Hermitian disordered systems
• Spectral and steady-state properties of fermionic random quadratic Liouvillians
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• An exactly solvable dissipative spin liquid
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions
• Universal hard-edge statistics of non-Hermitian random matrices
• Operator size growth in Lindbladian SYK
• Linear and Non-Linear Response of Quadratic Lindbladians
• Entanglement inside a black hole before the Page time
• Localization of Lindbladian Fermions
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Normal and superconducting currents through the Sachdev-Ye-Kitaev model
• Complexity of Quadratic Quantum Chaos
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Josephson current through the SYK model
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal