Niggemann, N.; Reuther, J.; Sbierski, B.: Quantitative functional renormalization for three-dimensional quantum Heisenberg models. SciPost Physics 12 (2022), p. 156/1-27
10.21468/scipostphys.12.5.156
Open Access Version
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 demon- strate a high quantitative accuracy of our method. Particularly, for the unfrustrated sim- ple cubic lattice antiferromagnet ordering temperatures obtained from finite-size scaling of one-loop data deviate from error controlled quantum Monte Carlo results by ∼ 5% and we confirm consistency of our data with established critical exponents ν and η 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 disor- dered 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 con- firm a finite width in the extrapolated limit T → 0. While extensions towards higher loop orders l seem to systematically improve our approach for magnetically disordered systems we also discuss subtleties when increasing l in the presence of magnetic or- der. 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.