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We implement an extension of the pseudofermion functional renormalizationgroup (PFFRG) method for quantum spin systems that takes into account two-loopdiagrammatic contributions. An efficient numerical treatment of the additionalterms is achieved within a nested graph construction which recombines differentone-loop interaction channels. In order to be fully self consistent withrespect to self-energy corrections we also include certain three-loop terms ofKatanin type. We first apply this formalism to the antiferromagnetic$J_1$-$J_2$ Heisenberg model on the square lattice and benchmark our resultsagainst the previous one-loop plus Katanin approach. Even though the RGequations undergo significant modifications when including the two-loop terms,the magnetic phase diagram -- comprising N\'eel ordered and collinear orderedphases separated by a magnetically disordered regime -- remains remarkablyunchanged. Only the boundary position between the disordered and the collinearphases is found to be moderately affected by two-loop terms. On the other hand,critical RG scales, which we associate with critical temperatures $T_\text{c}$,are reduced by a factor of $\sim2$ indicating that the two-loop diagrams play asignificant role in enforcing the Mermin-Wagner theorem. Improved estimates forcritical temperatures are also obtained for the Heisenberg ferromagnet on the3D simple cubic lattice where errors in $T_\text{c}$ are reduced by $\sim34\%$.

Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems