  In frustrated magnetism, making a stringent connection between microscopic
spin models and macroscopic properties of spin liquids remains an important
challenge. A recent step towards this goal has been the development of the
pseudofermion functional renormalization group approach (pf-FRG) which,
building on a fermionic parton construction, enables the numerical detection of
the onset of spin liquid states as temperature is lowered. In this work,
focusing on the SU(N) Heisenberg model at large N, we extend this approach in a
way that allows us to directly enter the low-temperature spin liquid phase, and
to probe its character. Our approach proceeds in momentum space, making it
possible to keep the truncation minimalistic, while also avoiding the bias
introduced by an explicit decoupling of the fermionic parton interactions into
a given channel. We benchmark our findings against exact mean-field results in
the large-N limit, and show that even without prior knowledge the pf-FRG
approach identifies the correct mean-field decoupling channel. On a technical
level, we introduce an alternative finite temperature regularization scheme
that is necessitated to access the spin liquid ordered phase. In a companion
paper arXiv:1711.02182 we present a different set of modifications of the
pf-FRG scheme that allow us to study SU(N) Heisenberg models (using a
real-space RG approach) for arbitrary values of N, albeit only up to the phase
transition towards spin liquid physics.
