Channel-decomposed solution of the parquet equations in the two-dimensional Hubbard model

The parquet equations are a set of selfconsistent equations for the effective interaction vertex of an interacting many-fermion system. The application of the parquet equations in bulk models is however complicated by the complex emergent momentum and frequency structure of the vertex. Here we show how channel-decomposition techniques for the treatment of the momentum dependence that were developed in the context of the functional renormalization group can be applied to the parquet equations. We describe solutions using this technique for the half-filled Hubbard model on the square lattice and discuss generalizations to other cases, as well as ways to include the frequency dependence of the vertices.