  We propose and study a two-orbital lattice extension of the Sachdev-Ye-Kitaev
model in the large-$N$ limit. The phase diagram of this model features a high
temperature isotropic strange metal which undergoes a first-order thermal
transition into a nematic insulator or a continuous thermal transition into
nematic metal phase, separated by a tunable tricritical point. These phases
arise from spontaneous partial orbital polarization of the multiorbital
non-Fermi liquid. We explore the spectral and transport properties of this
model, including the d.c. elastoresistivity, which exhibits a peak near the
nematic transition, as well as the nonzero frequency elastoconductivity. Our
work offers a useful perspective on nematic phases and transport in correlated
multiorbital systems.
