The shared universality of charged black holes and the many many-body SYK model

Abstract

We investigate the charged $q/2$-body interacting Sachdev-Ye-Kitaev (SYK) model in the grand-canonical ensemble. By treating $q$ as a large parameter, we are able to analytically study its phase diagram. By varying the chemical potential or temperature, we find that the system undergoes a phase transition between low and high entropies, in the maximally chaotic regime. A similar transition in entropy is seen in charged AdS black holes transitioning between a large and small event horizon. Approaching zero temperature, we find a first-order chaotic-to-non-chaotic quantum phase transition, where the finite extensive entropy drops to zero. This again has a gravitational analogue -- the Hawking-Page (HP) transition between a large black hole and thermal radiation. An analytical study of the critical phenomena associated with the continuous phase transition provides us with mean field van der Waals critical and effective exponents. We find that all analogous power laws are shared with several charged AdS black hole phase transitions. Together, these findings indicate a connection between the charged $q\to \infty$ SYK model and black holes.

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• Thermodynamics and dynamics of coupled complex SYK models
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model
• Gauging the complex SYK model