Spin fluctuations and pseudogap in the two-dimensional half-filled Hubbard model at weak coupling

Abstract

Starting from the Hubbard model in the weak-coupling limit, we derive a spin-fermion model where the collective spin excitations are described by a non-linear sigma model. This result is used to compute the fermion spectral function $A(\mathbf{k},\omega )$ in the low-temperature regime where the antiferromagnetic (AF) coherence length is exponentially large (``renormalized classical'' regime). At the Fermi level, $A({\mathbf{k}}_F,\omega )$ exhibits two peaks around $\pm {\Delta }_0$ (with ${\Delta }_0$ the mean-field gap), which are precursors of the zero-temperature AF bands, separated by a pseudogap.

6 pages, 2 figures, revised version