Incipient Antiferromagnetism and Low-Energy Excitations in the Half-Filled Two-Dimensional Hubbard Model

We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small $U$ are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\Sigma ({\mathbf{k}}_F,\varepsilon )$ and a local maximum in $|\mathrm{Im}\Sigma ({\mathbf{k}}_F,\varepsilon )|$ at $\varepsilon =0\mathrm{}$. We explain these results using a simple spin-fluctuation model.