Symmetry breaking in the S=1/2 and S=1 pyrochlore Heisenberg antiferromagnets

We investigate the ground-state properties of the nearest-neighbor S=1/2 and S=1 pyrochlore Heisenberg antiferromagnet using three complementary numerical methods, density-matrix renormalization group (DMRG), pseudofermion functional renormalization group (PFFRG) and numerical linked cluster expansion. Within DMRG, we are able to reliably study clusters with up to 128 spins (for S=1/2) and 48 spins (for S=1) by keeping 20 000 SU(2) states. Our most striking finding in the S=1/2 case is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra. We also determine the ground-state energy, E₀/N sites=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. In the S=1 case, the investigated 32-site and 48-site clusters both show indications of a robust C₃ 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 C₃ or a combined C₃/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the S=1/2 system.