Classical and quantum phases of the J₁-J₂-J₃ Heisenberg model on the body centered cubic lattice

We present the global phase diagram of the Heisenberg model on the body-centered cubic (BCC) lattice with nearest-neighbor J₁, second nearest-neighbor J₂ and third nearest-neighbor J₃ exchange couplings, for both antiferromagnetic and ferromagnetic J₁, J₂, and J₃. The classical phase diagram is shown to host four commensurate magnetic orders [ferromagnet q=(0,0,0), Néel antiferromagnet q=(2π,0,0), q=(π,π,0), and q=(π,π,π)], and three incommensurate helimagnetic orders, namely, a one-, two- and three-dimensional spiral. The corresponding quantum spin-1/2 model is investigated employing the pseudofermion functional renormalization group (PFFRG) method. It is shown that quantum fluctuations (i) stabilize a quantum spin liquid phase over an appreciable region in parameter space centered around tri-critical points, (ii) strongly renormalize the phase boundaries (compared to those of the classical model), (iii) shift the pitch vector of the helimagnetic orders. We obtain the critical ordering temperatures for the S=1/2 model from Quantum Monte Carlo in the unfrustrated parameter regime, and compare it with the estimates obtained from one- and two-loop PFFRG. In the frustrated regime of the model, we compare our estimates with results available from other methods.