Quantitative functional renormalization for three-dimensional quantum Heisenberg models
Nils Niggemann, Johannes Reuther, Björn Sbierski
SciPost Phys. 12, 156 (2022) · published 11 May 2022
- doi: 10.21468/SciPostPhys.12.5.156
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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 $\sim5\%$ and we further confirm the established values for the critical exponent $\nu$ and the anomalous dimension $\eta$. 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 $T\rightarrow0$. While extensions towards higher loop orders $\ell$ seem to systematically improve our approach for magnetically disordered systems we also discuss subtleties when increasing $\ell$ 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.
Cited by 17
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Nils Niggemann,
- 1 2 Johannes Reuther,
- 3 4 Björn Sbierski
- 1 Freie Universität Berlin / Freie Universität Berlin [FU Berlin]
- 2 Helmholtz-Zentrum Berlin für Materialien und Energie
- 3 Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU]
- 4 Munich Center for Quantum Science and Technology [MCQST]
- Deutsche Akademie der Naturforscher Leopoldina - Nationale Akademie der Wissenschaften (through Organization: Nationale Akademie der Wissenschaften Leopoldina / German National Academy of Sciences Leopoldina)
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]