Single-particle dispersion and density of states of the half-filled two-dimensional Hubbard model

Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half filling. At intermediate interactions of U/t=4, 6, we find quadratic dispersion around the gap minimum at wave vectors k= (/2, /2) (the points). We find saddle points at k= (, 0), (0, ) (the X points), where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to. The fraction of quasiparticle states within the ledge is n₋₄₃₆₄0. 15. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the points, with states around the X points becoming filled only at doping fractions xn₋₄₃₆₄. The high density of states away from the gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.