The Coupled SYK model at Finite Temperature

Abstract

Sachdev-Ye-Kitaev (SYK) model, which describes $N$ randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS${}_2$ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS${}_2$ geometry. This geometry is an "eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the $q$ dependence of the spectral function.

Note also an interesting parallel work on the revival dynamics in a traversable wormhole by S. Plugge, E. Lantagne-Hurtubise and M. Franz that appears in a parallel posting

References in corpus (1)

• Black holes as mirrors: quantum information in random subsystems

Cited by in corpus (18)

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• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Tunneling through an Eternal Traversable Wormhole
• Traversable wormhole in coupled SYK models with imbalanced interactions
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Probing quantum chaos in multipartite systems
• Chaos exponents of SYK traversable wormholes
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Soft modes in $\mathcal{N}=2$ SYK model
• Entropy Linear Response Theory with Non-Markovian Bath
• Excitation Transmission through a non-Hermitian traversable wormhole
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• On SYK traversable wormhole with imperfectly correlated disorders
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• $T\bar{T}$ deformation on non-Hermitian two coupled SYK model
• Towards Entanglement Entropy of Random Large-N Theories
• Sparse SYK and traversable wormholes
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model