Parquet approximation calculation for the 2D Hubbard model*

We present a numerical solution of the parquet approximation on a half-filled 4x4 Hubbard cluster. The parquet formalism is a two-particle self consistent set of equations relating the reducible, irreducible, and fully irreducible vertieces. The simplest approximation from this formalism is the so-called parquet approximation, in which the fully irreducible vertex is approximated by the bare interaction. Our results are compared with results from Self-Consistent 2nd-order approximation, Fluctuation Exchange (FLEX) approximation and the Determinental Quantum Monte Carlo (DQMC) calculation.