Single-Particle Dispersion and Density of States of the Half-Filled 2D 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 $U\mathrm{/}t=4,6$, we find quadratic dispersion around the gap minimum at wave-vectors $\mathbf{k}=(\pm \pi \mathrm{/}2,\pm \pi \mathrm{/}2)$ (the $\mathrm{\Sigma }$ points). We find saddle points at $\mathbf{k}=(\pm \pi ,0),(0,\pm \pi )$ (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 $\mathrm{\Sigma }$. The fraction of quasiparticle states within the ledge is $n_{\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}}\approx 0.15$. Upon doping away from half-filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\Sigma }$ points, with states around the X points becoming filled only at doping fractions $x\ge n_{\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}}$. The high density of states away from the $\mathrm{\Sigma }$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.