Taming pseudofermion functional renormalization for quantum spins: Finite temperatures and the Popov-Fedotov trick

The pseudofermion representation for $S=1/2$ quantum spins introduces unphysical states in the Hilbert space, which can be projected out using Popov-Fedotov trick. However, state-of-the-art implementation of functional renormalization group method pseudofermions have so far omitted projection. Instead, restrictions to zero temperature were made and absence contributions ground state was assumed. We question this belief by exact diagonalization several small-system counterexamples where do contribute state. then introduce projection renormalization, enabling finite-temperature computations with only minor technical modifications method. At large intermediate temperatures, our results are perturbatively controlled we confirm their accuracy benchmark calculations. lower degrades due truncation errors hierarchy flow equations. Interestingly, these problems cannot alleviated switching parquet approximation. spin as a method-intrinsic quality check. also show that magnetic-ordering transitions studied via finite-size scaling.