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Describing the emergence of phases of condensed matter is one of the centralchallenges in physics. For this purpose many numerical and analytical methodshave been developed, each with their own strengths and limitations. Thefunctional renormalization group is one of these methods bridging betweenefficiency and accuracy. In this paper we derive a new truncated unity (TU)approach unifying real- and momentum space TU, called TU$^2$FRG. This formalismsignificantly improves the scaling compared to conventional momentum (TU)FRGwhen applied to large unit-cell models and models where the translationalsymmetry is broken.

TU$^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models