We introduce a family of Gross-Neveu-Yukawa models with a large number of fermion and boson flavors as higher dimensional generalizations of the Sachdev-Ye-Kitaev model. The models may be derived from local lattice couplings and give rise to Lorentz invariant critical solutions in $1+1$ and $2+1$ dimensions. These solutions imply anomalous dimensions of both bosons and fermions tuned by the number ratio of boson to fermion flavors. In $1+1$ dimension the solution represents a stable critical phase, while in $2+1$ dimension it governs a quantum phase transition. We compute the out of time order correlators in the $1+1$ dimensional model, showing that it exhibits growth with the maximal Lyapunov exponent ${\lambda }_L=2\pi T$ in the low temperature limit.

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• Large-N expansion in field theory
• Quantum criticality
• Gross-Neveu model
• Sachdev-Ye-Kitaev model