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=(±π/2,±π/2) (the Σ points). We find saddle points at k=(±π,0),(0,±π) (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 Σ. The fraction of quasiparticle states within the ledge is nledge≈0.15. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the Σ points, with states around the X points becoming filled only at doping fractions x≥nledge. The high density of states away from the Σ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.