Sachdev-Ye-Kitaev (SYK) models describe 0+1 dimensional systems with random interactions between particles. Extensions of this model to higher dimensions have been found to produce linear in temperature resistivity, a mysterious property observed in strange metal phases. We study a two-band dispersive 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 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. See: Physical Review Research 4, 013145 (2022)

The ratio between the shear viscosity and the entropy is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that this ratio may violate the universal lower bound, scaling linearly with temperature in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly temperature independent, up to logarithmic scaling corrections, and can be extremely short for large nodal lines, near the Mott-Ragel-Ioffe limit. Our finding suggests that nodal-line semimetals can be very strongly correlated quantum systems. See more: Physical Review Research 3, 033003 (2021)