Abstract
A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state. We use adiabaticity arguments and numerical simulations to show that the character of the ground state remains unchanged when interaction strengths in the two SYK models become imbalanced. Analysis of thermodynamic and dynamical quantities highlights the key signatures of the wormhole phase in the imbalanced case. Further adiabatic evolution naturally leads to the ``maximally imbalanced'' limit where fermions in a single SYK model are each coupled to a free Majorana zero mode. This limit is interesting because it could be more easily realized using various setups proposed to implement the SYK model in a laboratory. We find, based on numerical studies of the quantum mechanical model, that this limiting case is marginal in that it retains some of the characteristic signatures of the wormhole physics, such as the spectral gap and revival dynamics, but lacks others so that it likely does not represent the full-fledged wormhole dual. We discuss how this scenario could be implemented in the proposed realization of the SYK physics in quantum wires of finite length coupled to a disordered quantum dot.
Highlights
The proposal of the SYK model [1,2,3] as a dual holographic description for a quantum black hole in (1+1) dimensional anti–de Sitter space AdS2 has motivated a flurry of research in scrambling of quantum information and many-body quantum chaos
While the thermofield double (TFD) inverse temperature βof the ground state depends on the coupling strength μ, we find βto be nearly independent of η
We find that the gap in the energy spectrum survives in the presence of this additional perturbation and only reduces in magnitude, indicating that the ground state for this setup is adiabatically connected to the η = 1 ground state found previously in the absence of the perturbation
Summary
The proposal of the SYK model [1,2,3] as a dual holographic description for a quantum black hole in (1+1) dimensional anti–de Sitter space AdS2 has motivated a flurry of research in scrambling of quantum information and many-body quantum chaos. Three key signatures of the wormhole phase have been identified in the literature: (i) the presence of the thermofield-double (TFD) ground state, (ii) a temperaturedriven first order phase transition of Hawking-Page type, and (iii) revival dynamics showing transmission of excitations between two maximally chaotic subsystems. We will investigate these indicators and find that all three persist in the imbalanced MQ model for η < 1.
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