Semi-classical simulation of spin-1 magnets

Abstract

Theoretical studies of magnets have traditionally concentrated on either classical spins, or the extreme quantum limit of spin-1/2. However, magnets built of spin-1 moments are also intrinsically interesting, not least because they can support quadrupole, as well as dipole moments, on a single site. For this reason, spin-1 models have been extensively studied as prototypes for quadrupolar (spin-nematic) order in magnetic insulators, and Fe-based superconductors. At the same time, because of the presence of quadrupoles, the classical limit of a spin-1 moment is not an $O(3)$ vector, a fact which must be taken into account in describing their properties. In this Article we develop a method to simulate spin-1 magnets based on a $u(3)$ algebra which treats both dipole and quadrupole moments on equal footing. This approach is amenable to both classical and quantum calculations, and we develop the techniques needed to calculate thermodynamic properties through Monte Carlo simulations and classical low-temperature expansion, and dynamical properties, through "molecular dynamics" simulations and a multiple-boson expansion. As a case study, we present detailed analytic and numerical results for the thermodynamic properties of ferroquadrupolar order on the triangular lattice, and its associated dynamics. At low temperatures, we show that it is possible to "correct" for the effects of classical statistics in simulations, and extrapolate to the zero-temperature quantum results found in flavour-wave theory.

66 pages and 24 figures

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Cited by in corpus (20)

• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Langevin dynamics of generalized spins as SU($N$) coherent states
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Material-based analysis of spin-orbital Mott insulators
• Gravitational wave analogues in spin nematics and cold atoms
• Revealing Quadrupolar Excitations with Non-Linear Spectroscopy
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• Emergence of Elastic Softening Featuring Ultra-Slow Dynamics Around Magnetic Critical Endpoint in UCoAl
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Quantum Fluctuations in the van der Walls material $\mathrm{NiP}{\mathrm{S}}_3$
• Orbital moiré and quadrupolar triple-q physics in a triangular lattice
• Emulation of quantum correlations by classical dynamics in a spin-1/2 Heisenberg chain
• Thermal Ising transition in two-dimensional SU(3) Fermi lattice gases with population imbalance
• Nonabelian ferromagnets with three-body interactions
• Demystifying quantum escapism on the honeycomb lattice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States
• Adjoint ferromagnets
• $SU(N)$ spin-phonon simulations of Floquet dynamics in spin $S>1/2$ Mott insulators