Note on entropy dynamics in the Brownian SYK model
arXiv:2011.08158 · doi:10.1007/JHEP03(2021)042
Abstract
We study the time evolution of Rényi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The Rényi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of Rényi entropy, respectively.
arXiv comment33 pages
References in corpus (24)
- Comments on the Sachdev-Ye-Kitaev model
- Average Entropy of a Subsystem
- Replica Wormholes and the Entropy of Hawking Radiation
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- The Page curve of Hawking radiation from semiclassical geometry
- Towards the fast scrambling conjecture
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Emergent statistical mechanics of entanglement in random unitary circuits
- Entanglement islands in higher dimensions
- Islands in Schwarzschild black holes
- Islands in cosmology
- Bra-ket wormholes in gravitationally prepared states
- Page Curve for an Evaporating Black Hole
- Islands in Asymptotically Flat 2D Gravity
- Islands in de Sitter space
- Notes on islands in asymptotically flat 2d dilaton black holes
- Quantum chaos in the Brownian SYK model with large finite : OTOCs and tripartite information
- Entanglement between two disjoint universes
- A Random Unitary Circuit Model for Black Hole Evaporation
- Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
- Correlations in Hawking radiation and the infall problem
- One-shot decoupling and Page curves from a dynamical model for black hole evaporation
- Black Holes as Rubik's Cubes
- Quantum Circuit Model of Black Hole Evaporation
Cited by in corpus (22)
- SYK meets non-Hermiticity II: measurement-induced phase transition
- Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Emergent Replica Conformal Symmetry in Non-Hermitian SYK Chains
- Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
- Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
- Information Scrambling with Conservation Laws
- Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
- Designs via Free Probability
- Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
- Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
- Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry
- Strong-to-weak Symmetry Breaking and Entanglement Transitions
- Thermalization of Randomly Coupled SYK Models
- Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models
- Entanglement inside a black hole before the Page time
- Field theory for monitored Brownian SYK clusters
- Efficient circular Dyson Brownian motion algorithm
- Entanglement dynamics from universal low-lying modes
- Dynamics in the presence of local symmetry-breaking impurities
- Chaos-protected locality
- Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos