SYK Model, Chaos and Conserved Charge

Abstract

We study the SYK model with complex fermions, in the presence of an all-to-all $q$-body interaction, with a non-vanishing chemical potential. We find that, in the large $q$ limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential $\mu$. Even when the coupling $J$, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of $\mu$ which are exponentially small compared to $J$ lead to suppression of the Lyapunov exponent.

arXiv comment18pages, 4 figures, v2:references and acknowledgment added, typos corrected

References in corpus (29)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Black Holes and Random Matrices
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Fermionic Localization of the Schwarzian Theory
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Bi-Local Holography in the SYK Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• The complete $1/N$ expansion of a SYK--like tensor model
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• Towards a 2d QFT Analog of the SYK Model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• SYK-like Tensor Models on the Lattice
• On Large $N$ Limit of Symmetric Traceless Tensor Models
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Towards a Finite-$N$ Hologram
• A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling

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• On the Dynamics of Near-Extremal Black Holes
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Thouless time for mass-deformed SYK
• A note on the complex SYK model and warped CFTs
• Diffusion in higher dimensional SYK model with complex fermions
• Towards the Holographic Dual of N = 2 SYK
• Phase transition and chaos in charged SYK model
• Supersymmetric SYK Model with Global Symmetry
• When things stop falling, chaos is suppressed
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Thermalization of many many-body interacting SYK models
• Rotating Black Holes in AdS, Extremality and Chaos
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• On Melonic Supertensor Models
• Exact Embeddings of JT Gravity in Strings and M-theory
• What is the Simplest Linear Ramp?
• Spectral form factor in the double-scaled SYK model
• Unraveling the emergence of quantum state designs in systems with symmetry
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Thermalization in different phases of charged SYK model
• Holography, quantum complexity and quantum chaos in different models
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Thermodynamics and dynamics of coupled complex SYK models
• Chaotic Correlation Functions with Complex Fermions
• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• SYK Model with global symmetries in the double scaling limit
• A route from maximal chaoticity to integrability
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models