  QCD at large density reveals a rich phase structure, ranging from a potential
critical end point and inhomogeneous phases or moat regimes to color
superconducting ones with competing order effects. Resolving this region in the
phase diagram of QCD with functional approaches requires a great deal of
quantitative reliability, already for a qualitative access. In the present
work, we systematically extend the functional renormalisation group approach to
low energy QCD by setting up a fully self-consistent approximation scheme in a
low energy effective quark-meson theory. In this approximation, all pointlike
multi-scattering events of the mesonic pion and the sigma mode are taken into
account in terms of an effective potential as well as all higher
quark-antiquark-mesonic scattering orders. As a first application we compute
the phase structure of QCD including its low temperature - large chemical
potential part. The quantitative reliability of the approximation and
systematic extensions are also discussed.
