Fluctuations and going beyond mean field theory in the triangular lattice Hubbard model

Mean field theory techniques have been and continue to be widely applied

in the study of strongly correlated many-body systems. For these systems, the advantage

of mean field theory comes from fact that it provides qualitative, and sometimes quantitative,

information on the tendency of the many-body system to develop ordered phases when

other theoretical methods might not apply. However, the strength of its wide use

comes at the cost of ignoring fluctuations in the relevant degrees of freedom of

the model. Hence, ordered phases found from a mean field study of a model Hamiltonian

may not be stable when fluctuations are included. In recent Hartree-Fock mean field

calculations for the Hubbard model on the triangular lattice at electron density n = 2/3,

we found a charge-ordered collinear antiferromagnetic phase on the honeycomb

sublattice above a critical interaction, U_c/t. The geometric frustration inherent to  

the triangular lattice enhances fluctuations in the Hubbard model. Therefore, we discuss

different numerical methods that incorporate fluctuations and how they can

be applied to the n = 2/3 triangular lattice Hubbard model. We present preliminary results

from numerical calculations.