Quantitative functional renormalization for three-dimensional quantum Heisenberg models

Niggemann, Nils; Reuther, Johannes und Sbierski, Björn (2022): Quantitative functional renormalization for three-dimensional quantum Heisenberg models. In: Scipost Physics, Bd. 12, Nr. 5, 156

Abstract

We employ a recently developed variant of the functional renormalization group method for spin systems, the so-called pseudo Majorana functional renormalization group, to investigate three-dimensional spin-1/2 Heisenberg models at finite temperatures. We study unfrustrated and frustrated Heisenberg systems on the simple cubic and pyrochlore lattices. Comparing our results with other quantum many-body techniques, we demonstrate a high quantitative accuracy of our method. Particularly, for the unfrustrated simple cubic lattice antiferromagnet ordering temperatures obtained from finite-size scaling of one-loop data deviate from error controlled quantum Monte Carlo results by similar to 5% and we confirm consistency of our data with established critical exponents nu and eta of the three-dimensional Heisenberg universality class. As the PMFRG yields results in good agreement with QMC, but remains applicable when the system is frustrated, we next treat the pyrochlore Heisenberg antiferromagnet as a paradigmatic magnetically disordered system and find nearly perfect agreement of our two-loop static homogeneous susceptibility with other methods. We further investigate the broadening of pinch points in the spin structure factor as a result of quantum and thermal fluctuations and confirm a finite width in the extrapolated limit T -> 0. While extensions towards higher loop orders 'seem to systematically improve our approach for magnetically disordered systems we also discuss subtleties when increasing ` in the presence of magnetic order. Overall, the pseudo Majorana functional renormalization group is established as a powerful many-body technique in quantum magnetism with a wealth of possible future applications. Published by the SciPost Foundation.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 2542-4653
• Sprache: Englisch