Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet

We investigate the ground-state properties of the nearest-neighbor $S=1$ pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust $C_3$ rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either $C_3$ or a combined $C_3$/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the $S=1\mathrm{/}2$ system.