Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals

Understand

We study a sparse Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas where only $\sim k N$ independent matrix elements are non-zero.

• We identify a minimum $k \gtrsim 1$ for quantum chaos to occur by a level statistics analysis.
• The spectral density in this region, and for a larger $k$, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters.
• Similar results are obtained for a beyond linear scaling with $N$ of the number of non-zero matrix elements.