Multiflavor SYK model on the lattice

The Sachdev-Ye-Kitaev (SYK) model is a canonical solvable model of a non-Fermi liquid. We study the physics of a multiflavor SYK model on the lattice and discuss its spectral properties in the presence and absence of particle-hole symmetry breaking. These flavours, which can be thought of as emulating fermion spins or orbitals, along with the underlying lattice, connect the phases observed in our model to intriguing experimental observations. Using numerical and analytic calculations, we illustrate the existence of quantum phase transitions and multicritical phenomena in our model, and discuss transport properties in the large-N limit.