Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model

TL;DR

This paper investigates the phase diagram of the 3D Hubbard model on a cubic lattice, revealing a non-magnetic insulating phase likely representing a quantum spin liquid, using variational cluster and spin-wave theories.

Contribution

It identifies a non-magnetic insulating region in the 3D Hubbard model, suggesting the existence of a quantum spin liquid in three dimensions, which is a novel finding.

Findings

Discovery of a non-magnetic insulating phase in the phase diagram.

Establishment of the phase diagram for the related Heisenberg model.

Similarity to 2D spin-liquid behavior in a 3D context.

Abstract

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 non-magnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the large-$U$ limit, we establish the phase diagram of the corresponding $J_1$-$J_2$-$J_3$ Heisenberg model. This is qualitatively confirmed - including the non-magnetic region - using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the $J_1$-$J_2$ square-lattice Heisenberg model, suggesting that the non-magnetic region hosts a 3D spin-liquid phase.