Magnetic properties and temperature variation of spectra in the Hubbard model

In the two-dimensional fermionic Hubbard model, temperature and concentration dependencies of the uniform magnetic susceptibility and squared site spin, the variation of the double occupancy with the repulsion and the temperature dependence of the spin structure factor are calculated using the strong coupling diagram technique. In these calculations, a correction parameter is introduced into the irreducible vertex to fulfill the Mermin-Wagner theorem and to attain low temperatures. Satisfactory agreement of the obtained results with data of Monte Carlo simulations, numerical linked-cluster expansions and experiments in optical lattices lends support to the validity of such a correction. The ability to attain low temperatures allows us to investigate spectral functions in this region. At half-filling, for small and large Hubbard repulsions no qualitative changes are observed in comparison with somewhat higher temperatures reached in the previous work. However, on cooling, there appears a new feature for moderate repulsions – a narrow band emerges near the Fermi level, which produces a pronounced peak in the density of states. By its location and bandwidth, the feature is identified with the spin-polaron band. Graphical abstract