Abstract
The canonical one-band Hubbard model is studied using a computational method that mixes the Monte Carlo
procedure with themean field approximation. This technique allows us to incorporate thermal fluctuations and the
development of short-range magnetic order above ordering temperatures, contrary to the crude finite-temperature
Hartree-Fock approximation, which incorrectly predicts a N´eel temperature TN that grows linearly with the
Hubbard U/t . The effective model studied here contains quantum and classical degrees of freedom. It thus
belongs to the “spin fermion” model family widely employed in other contexts. Using exact diagonalization,
supplemented by the traveling cluster approximation, for the fermionic sector, and classical Monte Carlo for
the classical fields, the Hubbard U/t vs temperature T/t phase diagram is studied employing large three- and
two-dimensional clusters.We demonstrate that the method is capable of capturing the formation of local moments
in the normal state without long-range order, the nonmonotonicity of TN with increasing U/t , the development
of gaps and pseudogaps in the density of states, and the two-peak structure in the specific heat. Extensive
comparisons with determinant quantum Monte Carlo results suggest that the present approach is qualitatively,
and often quantitatively, accurate, particularly at intermediate and high temperatures. Finally, we study the
Hubbard model including plaquette diagonal hopping (i.e., the t -t
Hubbard model) in two dimensions and show
that our approach allows us to study low-temperature properties where determinant quantum Monte Carlo fails
due to the fermion sign problem. Future applications of this method include multiorbital Hubbard models such
as those needed for iron-based superconductors.
