A case study of spin-$1$ Heisenberg model in a triangular lattice

Abstract

We study the spin-$1$ model in a triangular lattice in presence of a uniaxial anisotropy field using a Cluster Mean-Field approach (CMF). The interplay between antiferromagnetic exchange, lattice geometry and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF yields two supersolid (SS) phases compatible with those present in the spin-$1/2$ XXZ model onto which the spin-$1$ system maps. Between these two SS phases, the three-sublattice order is broken and the results of the CMF depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

7 pages, 4 figures, RevTeX 4. The abstract and conclusions have been modified and the manuscript has been extended

References in corpus (8)

• Supersolid hardcore bosons on the triangular lattice
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Quantum phases of hardcore bosons with long-range interactions on a square lattice
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• Quantum Phases of Trapped Ions in an Optical Lattice
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• Competing quantum phases of hard-core boson with tilted dipole-dipole interaction
• Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice
• Magnetization process of spin-1/2 Heisenberg antiferromagnets on a layered triangular lattice
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• Magnetic phases of spin-1 lattice gases with random interactions
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
• Induced quantum magnetism on a triangular lattice of non-Kramers ions in PrMgAl11O19
• Using Random Boundary Conditions to simulate disordered quantum spin models in 2D-systems
• Emergent Spin Supersolids in Frustrated Quantum Materials
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