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

Schneider, Benedikt; Kiese, Dominik und Sbierski, Bjorn (2022): Taming pseudofermion functional renormalization for quantum spins: Finite temperatures and the Popov-Fedotov trick. In: Physical Review B, Bd. 106, Nr. 23, 235113

Abstract

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

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 2469-9950
• Sprache: Englisch