Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

Abstract

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with a $q$-body interaction of infinite range, coupled to a Markovian environment. Close to the infinite-temperature steady state, the real-time Lindbladian dynamics of this system is identical to the near-zero-temperature dynamics in Euclidean time of a two-site non-Hermitian SYK with intersite coupling whose gravity dual has been recently related to wormhole configurations. We show that the saddle-point equations in the real-time formulation are identical to those in Euclidean time. Indeed, an explicit calculation of Green's functions at low temperature, numerical for $q=4$ and analytical for $q=2$ and large $q$, illustrates this equivalence. Only for very strong coupling does the decay rate approach the linear dependence on the coupling characteristic of a dissipation-driven approach to the steady state. For $q>2$, we identify a potential gravity dual of the real-time dissipative SYK model: a double-trumpet configuration in a near-de Sitter space in two dimensions with matter. This configuration, which we term a Keldysh wormhole, is responsible for a finite decay rate even in the absence of coupling to the environment.

52 pages, 9 figures. v2: added comments to explain a possible connection with dS${}_2$ and improved the finite-$N$ calculations and their interpretation. v3: minor corrections, references added, version as published

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Cited by in corpus (25)

• Quantum Dynamics in Krylov Space: Methods and Applications
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• Dynamical quantum phase transitions in SYK Lindbladians
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Spectral and steady-state properties of fermionic random quadratic Liouvillians
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Theory of Irreversibility in Quantum Many-Body Systems
• Operator size growth in Lindbladian SYK
• Entanglement inside a black hole before the Page time
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Phases of Euclidean wormholes in JT gravity
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Error bounds on the universal Lindblad equation in the thermodynamic limit
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems