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.

28 pages, 9 figures. References added

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Cited by in corpus (33)

• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Dispersive SYK model: band structure and quantum chaos
• Lindbladian dissipation of strongly-correlated quantum matter
• 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
• Towards a Finite-$N$ Hologram
• Universal Constraints on Energy Flow and SYK Thermalization
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid
• Page Curve from Non-Markovianity
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Operator size growth in Lindbladian SYK
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• More on Complex Sachdev-Ye-Kitaev Eternal Wormholes
• Lyapunov exponents in a Sachdev-Ye-Kitaev-type model with population imbalance in the conformal limit and beyond
• Quasiparticle tunnelling in two coupled chiral SYK model
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics