Non-Local Corrections to the Dynamical Mean Field Theory for the Hubbard Model

We use the diagrammatic parquet formalism to calculate the non-local corrections to the Dynamical Mean Field Theory ($DMFT$) solution for the two-dimensional Hubbard model. The Dynamical Mean Field Theory vertex and Green's function are used as input to calculate the Feynman diagrams on a finite size cluster. This approach properly addresses the local as well as the short-range correlations, as illustrated by the agreement of the obtained local moment and the Neel critical temperature with Quantum Monte Carlo calculations on a $4$x$4$ cluster.