In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength $U$ and various antiferromagnetic insulators at large $U$, we find an intermediate-$U$ antiferromagnetic metal. Most interestingly, we also identify a nonmagnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the large-$U$ limit, we establish the phase diagram of the corresponding $J_1\text{−}{J}_2\text{−}{J}_3$ Heisenberg model. This is qualitatively confirmed—including the nonmagnetic region—using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the $J_1\text{−}{J}_2$ square-lattice Heisenberg model, suggesting that the nonmagnetic region may host a 3D spin-liquid phase.

• Received 2 July 2015
• Revised 5 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.041106