Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model

• DOI: 10.48550/arxiv.2405.12745
• Publication Date: 2024-01-01
• Authors: Hagymási, Imre; Niggemann, Nils; Reuther, Johannes
• Keywords: Condensed Matter - Strongly Correlated Electrons; Density matrix renormalization group; Moderne Physik; Strongly Correlated Electrons (cond-mat.str-el); Frustrated magnetism; 539; FOS: Physical sciences; Matrix product states; Functional renormalization group

13 pages, 10 figures<br/>We study the phase diagram of the antiferromagnetic $J_1$-$J_2$ 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 present an efficient approach to preserve the applicability of the PMFRG for spin-1 systems at finite temperatures despite the inevitable presence of unphysical spin states. The good performance of our methods is first demonstrated for 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 $J_2/J_1 \sim 0.02 $ within DMRG, beyond which magnetic $\boldsymbol{k}=0$ long-range order sets in. Our PMFRG calculations find the phase transition in a similar regime $J_2/J_1\sim 0.035(8)$ 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. We also discuss the origin of discrepancies between different versions of the functional renormalization group concerning the location of this phase transition.<br/>