Spin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study

Abstract

We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.

7 pages, 8 figures

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• Semi-classical simulation of spin-1 magnets
• Finding hidden order in spin models with persistent homology
• Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice
• Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems
• A numerical study of the 3D random interchange and random loop models
• Probing Hidden Orders with Resonant Inelastic X-Ray Scattering
• Gravitational wave analogues in spin nematics and cold atoms
• Pronounced 2/3 magnetization plateau in a frustrated $S$ = 1 isolated spin-triangle compound: Interplay between Heisenberg and biquadratic exchange interactions
• Finite temperature thermodynamic properties of the spin-1 nematics in an applied magnetic field
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• Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain
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• Quadrupolar quantum criticality on a fractal