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In frustrated magnetism, making a stringent connection between microscopicspin models and macroscopic properties of spin liquids remains an importantchallenge. A recent step towards this goal has been the development of thepseudofermion functional renormalization group approach (pf-FRG) which,building on a fermionic parton construction, enables the numerical detection ofthe 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 away that allows us to directly enter the low-temperature spin liquid phase, andto probe its character. Our approach proceeds in momentum space, making itpossible to keep the truncation minimalistic, while also avoiding the biasintroduced by an explicit decoupling of the fermionic parton interactions intoa given channel. We benchmark our findings against exact mean-field results inthe large-N limit, and show that even without prior knowledge the pf-FRGapproach identifies the correct mean-field decoupling channel. On a technicallevel, we introduce an alternative finite temperature regularization schemethat is necessitated to access the spin liquid ordered phase. In a companionpaper arXiv:1711.02182 we present a different set of modifications of thepf-FRG scheme that allow us to study SU(N) Heisenberg models (using areal-space RG approach) for arbitrary values of N, albeit only up to the phasetransition towards spin liquid physics.

Functional renormalization group approach to SU(N) Heisenberg models: Momentum-space RG for the large-N limit