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The parquet approach to vertex corrections is unbiased but computationallydemanding. Most applications are therefore restricted to small cluster sizes orrely on various simplifying approximations. We have recently shown that thebosonization of the parquet diagrams provides interpretative and algorithmicadvantages over the original purely fermionic formulation. Here we presentfirst results of the numerical implementation of this method by applying it tothe half-filled Hubbard model on the square lattice at weak coupling. Theimproved algorithmic performance allows us to evaluate the parquetapproximation for a $16\times16$ lattice, retaining the full momentum andfrequency structure of the various vertex functions. We discuss theirsymmetries and consider parametrizations of their momentum dependence using thetruncated unity approximation.

The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model