The Sachdev-Ye-Kitaev Model and Quantum Chaos in Many-Body Systems
The Sachdev-Ye-Kitaev model was originally introduced in nuclear physics by French and Mon
to describe the spectral properties of complex nuclei. In condensed matter physics it was
proposed as a model for a spin liquid by Sachdev and Ye, but the model only really took off a
few years ago after Kitaev introduced it as a model for a black hole. The SYK model is a
paradigm for a non-Fermi liquid which has a zero temperature entropy that is extensive with
a level density that increases exponentially with energy. Because, in addition the model is
chaotic, it has the necessary ingredients for being a quantum mechanical model of a black hole.
In this lecture, we give an elementary introduction of the SYK model, discuss its chaotic
properties in terms of level correlations, and explain the relevant time scales.
In a coupled SYK model that has been proposed as model for a wormhole we find that
eigenstate thermalization gives a good description of the ground state of this model.
Department of Physics