Phase diagram of the antiferromagnetic J₁-J₂ spin-1 pyrochlore Heisenberg model

We investigate the phase diagram of the antiferromagnetic J₁-J₂ Heisenberg model on the pyrochlore lattice with S=1 spins at zero and finite temperatures. We use a combination of complementary state-of-the-art quantum many-body approaches such as density matrix renormalization group (DMRG), density-matrix purification and pseudo-Majorana functional renormalization group (PMFRG). We address first the nearest-neighbor pyrochlore Heisenberg model where the finite temperature behavior of the specific heat and uniform susceptibility show excellent agreement within PMFRG and density-matrix purification. Including an antiferromagnetic second neighbor coupling we find that the non-magnetic ground-state phase of the nearest neighbor model extents up to J₂/J₁ ~ 0.02 within DMRG, beyond which magnetic k=0 long-range order sets in. Our PMFRG calculations find the phase transition in a similar regime J₂/J₁ ~ 0.035(8) which, together with the DMRG result, provides a strong argument for the existence of a small but finite non-magnetic ground-state phase in the spin-1 pyrochlore Heisenberg model.