  Abstract We study a two-band dispersive Sachdev-Ye-Kitaev (SYK) model in 1 +
1 dimension. We suggest a model that describes a semimetal with quadratic
dispersion at half-filling. We compute the Green's function at the saddle point
using a combination of analytical and numerical methods. Employing a scaling
symmetry of the Schwinger-Dyson equations that becomes transparent in the
strongly dispersive limit, we show that the exact solution of the problem
yields a distinct type of non-Fermi liquid with sublinear $\rho\propto T^{2/5}$
temperature dependence of the resistivity. A scaling analysis indicates that
this state corresponds to the fixed point of the dispersive SYK model for a
quadratic band touching semimetal.
