Quantum Phase Diagram and Quantum Monte Carlo Study of the XYZ Spin Model: The Dipole-octupole Doublets on a Triangular Lattice

Motivated by the recent activities on the geometrically frustrated rare-earth magnets, we study the quantum phase diagram of the XYZ spin model that describes the dipole-octupole doublets on a triangular lattice. Due to the absence of the sign problem of this model in a large parameter regime, we carry out the first quantum Monte Carlo calculation with the stochastic series expansion method and obtain the magnetic ground states with and without the external magnetic fields. The combination of the geometrical frustration and the anisotropic spin interaction leads to a rather rich phase diagram with a multitude of symmetry breaking orders. Moreover, the multipolar nature of the dipole-octupole doublet brings new ingredients for the quantum fluctuations in the ordered phases. The experimental relevance to the rare-earth triangular lattice materials is discussed.