Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath

Abstract

The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with $N$ Majorana fermion modes coupled to another SYK model with $N^2$ Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from $2\pi /\beta$ ($\beta =1/(k_{B}T)$, $T$ is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a $\sqrt{T}$-dependence at relatively high temperature to a linear $T$-dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

arXiv comment28 pages, 9 figures. References added

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Cited by in corpus (52)

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• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Dispersive SYK model: band structure and quantum chaos
• A Random Unitary Circuit Model for Black Hole Evaporation
• Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
• Lindbladian dissipation of strongly-correlated quantum matter
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Phases Of Melonic Quantum Mechanics
• Contrasting SYK-like Models
• Towards the Holographic Dual of N = 2 SYK
• A new class of SYK-like models with maximal chaos
• Towards a Finite-$N$ Hologram
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Thermal Diffusion and Quantum Chaos in Neutral Magnetized Plasma
• Universal Constraints on Energy Flow and SYK Thermalization
• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Family of Sachdev-Ye-Kitaev models motivated by experimental considerations
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• The chiral SYK model
• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• Conformality of $1/N$ corrections in SYK-like models
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Page Curve from Non-Markovianity
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Chiral Algebras of Two-Dimensional SYK Models
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
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• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
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