Numerically efficient parquet-equations solver for correlated electron systems*

The parquet equations are a set of self-consistent equations for the effective
interaction vertex of an interacting many-fermion system [1].
Their numerical solution has, however, been plagued by the extreme memory
consumption of the vertex functions, even for small systems.
We use the truncated-unity method, previously developed in the
context of the functional renormalization group (fRG), to approximate
the complex emergent momentum structure of the vertex [2].
There, the full momentum dependence of the vertex is projected onto
few formfactors.
By these means, we can reduce the memory needed to solve the parquet
equations by several orders of magnitude.
This makes the parquet-approach a useful tool to calculate two particle properties in the parquet approximation
and as nonlocal corrections to Dynamical Mean Field Theory (DMFT) calculations (parquet Dynamical Vertex Approximation)[3].
We will show results for the two-dimensional Hubbard model and
comparisons with the ladder-Dynamical Vertex Approximation and fRG methods.

[1] Gang, Li et al., arxiv.org/abs/1708.07457, (2017)
[2] Eckhardt et al., Phys. Rev. B 98, 075143, (2018)
[3] Rohringer et al., Rev. Mod. Phys. 90, 025003, (2018)