Interconnected renormalization of Hubbard bands and Green's function zeros in Mott insulators induced by strong magnetic fluctuations

We analyze the role of spatial electronic correlations and, in particular, of the magnetic fluctuations in Mott insulators. A half-filled Hubbard model is solved at large strength of the repulsion $U$ on a two-dimensional square lattice using an advanced diagrammatic approach capable of going beyond Hartree-Fock and single-site dynamical mean-field theories. We show that at high temperatures, when the magnetic fluctuations are weak, the electronic self-energy of the system is mainly local and is well reproduced by the atomic (Hubbard-I) approximation. Upon lowering the temperature toward the magnetically ordered phase, the nonlocality of the self-energy becomes crucial in determining the momentum dispersion of the Hubbard bands and the Green's function zeros. We therefore establish a precise link between Luttinger surface, nonlocal correlations and spectral properties of the Hubbard bands.