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

TL;DR

This paper investigates the phase diagram of the spin-1 antiferromagnetic $J_1$-$J_2$ pyrochlore Heisenberg model using advanced quantum many-body methods, revealing a small non-magnetic phase and magnetic order transition.

Contribution

It introduces an efficient approach to apply PMFRG to spin-1 systems at finite temperatures and combines multiple methods to identify the non-magnetic phase boundary.

Findings

Non-magnetic ground state persists up to $J_2/J_1 \\sim 0.02$ (DMRG)

Magnetic order appears beyond $J_2/J_1 \\sim 0.035$ (PMFRG)

Strong agreement between PMFRG and DMRG results on phase boundary

Abstract

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.