SYK criticality and spin glass order in the random doped Heisenberg model

We investigate the t-J model of electrons with fully connected random hoppings and exchange interactions. Using numerical exact diagonalization and the thermal pure quantum state method, we establish the extent of the spin glass ordered known to be present at half-filling is stable to non-zero hole doping, up to a critical hole-doping of around $p_c =1/3$. Our simulations reveal a maximum of the thermodynamic entropy at finite temperature as well as a maximum of the entanglement entropy at zero temperature close to $p_c$. The quasiparticle spectral density is found to obey the analog of the Fermi liquid Luttinger relation only for p > p_c. We note connections to SYK criticality and the hole-doped cuprates.