SYK non-Fermi-liquid solution of the Hubbard model*

The bold-line diagrammatic technique solution of the Hubbard model in the strong coupling regime is of an SYK non-Fermi-liquid (nFL) type, obtained in a controlled way by the numerically exact diagrammatic Monte Carlo method. In the atomic (zero-hopping) limit, the solution corresponds to the unphysical branch of the Luttinger-Ward functional, for which the SYK model is the exact solution at the second order. Interestingly, the Green’s function retains its scaling form at higher orders. The solution for the doped 2d Hubbard model features an SYK-type nFL regime in a wide intermediate temperature range enclosed by the low-temperature Fermi-liquid and the high-temperature atomic limit. The possibility of SYK physics taking place in the Hubbard model is discussed.