Quantitative functional renormalization for three-dimensional quantum Heisenberg models

We employ a recently developed variant of the functional renormalization group method for spin systems, so-called pseudo Majorana group, to investigate three-dimensional spin-1/2 Heisenberg models at finite temperatures. study unfrustrated and frustrated systems on simple cubic pyrochlore lattices. Comparing our results with other quantum many-body techniques, we demonstrate high quantitative accuracy method. Particularly, lattice antiferromagnet ordering temperatures obtained from finite-size scaling one-loop data deviate error controlled Monte Carlo by $\sim5\%$ further confirm established values critical exponent $\nu$ anomalous dimension $\eta$. As PMFRG yields in good agreement QMC, but remains applicable when system is frustrated, next treat as paradigmatic magnetically disordered find nearly perfect two-loop static homogeneous susceptibility methods. broadening pinch points structure factor result thermal fluctuations width extrapolated limit $T\rightarrow0$. While extensions towards higher loop orders $\ell$ seem systematically improve approach also discuss subtleties increasing presence magnetic order. Overall, powerful technique magnetism wealth possible future applications.