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.

arXiv comment66 pages and 24 figures

References in corpus (70)

• Cold bosonic atoms in optical lattices
• Parallel Tempering: Theory, Applications, and New Perspectives
• Nematic order in iron superconductors - who is in the driver's seat?
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Spin-lattice coupling in frustrated antiferromagnets
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Ultracold fermions and the SU(N) Hubbard model
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Spinor Bosonic Atoms in Optical Lattices: Symmetry Breaking and Fractionalization
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S=1$ quantum spin-liquids based on Ni^{2+}
• Dimer state of spin-1 Bosons in an optical lattice
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Possible ferro-spin nematic order in NiGa2S4
• Effective field theory for S=1 quantum nematic
• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Waves in the unseen : theory of spin excitations in a quantum spin nematic
• Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi${}_2$F${}_7$
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• Hybridized quadrupolar excitations in the spin-anisotropic frustrated magnet FeI2
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• The bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect
• Spin Liquid Phases for Spin-1 systems on the Triangular lattice
• Evidence for a spinon Fermi surface in the triangular S=1 quantum spin liquid Ba${}_3$NiSb${}_2$O${}_9$
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Exotic S=1 spin liquid state with fermionic excitations on triangular lattice
• Mott transitions in ternary flavor mixtures of ultracold fermions on optical lattices
• Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
• Field-induced phase transitions of repulsive spin-1 bosons in optical lattices
• Spin nematic order in antiferromagnetic spinor condensates
• Ghost in the machine: Theory of inelastic neutron scattering in a field-induced spin-nematic state
• Classical spin dynamics based on SU($N$) coherent states
• Frustrated Spin One On A Diamond Lattice
• Semiclassical dynamics of spin density waves
• Dynamics and relaxation in spin nematics
• Coherent Behavior and Nonmagnetic Impurity Effects of the Spin Disordered State in NiGa${}_2$S${}_4$
• A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
• Frustrated quantum critical theory of putative spin-liquid phenomenology in 6H-B-Ba3NiSb2O9
• Spin Ferroquadrupolar Order in the Nematic Phase of FeSe
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Pairing of Solitons in Two-Dimensional S=1 Magnets
• Spin nematic ground state of the triangular lattice S=1 biquadratic model
• Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics
• How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?
• Possible Nematic Spin Liquid in Spin-$1$ Antiferromagnetic System on the Square Lattice: Implication for the Nematic Paramagnetic State of FeSe
• Direct observation of spin-quadrupolar excitations in Sr${}_2$CoGe${}_2$O${}_7$ by high field ESR
• Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice
• A non-abelian spin-liquid in a spin-1 quantum magnet
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• Spin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study
• Antiferroquadrupolar order and rotational symmetry breaking in a generalized bilinear-biquadratic model on a square lattice
• Impact of the lattice on magnetic properties and possible spin nematicity in the S=1 triangular antiferromagnet NiGa${}_2$S${}_4$
• Spin and quadrupolar orders in the spin-1 bilinear-biquadratic model for iron-based superconductors
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Anderson tower of states and nematic order of spin-1 bosonic atoms on a 2D lattice
• Three-dimensional nematic spin liquid in the stacked triangular lattice 6H-B structure
• Understanding temperature-dependent SU($3$) spin dynamics in the $S=1$ antiferromagnet Ba${}_2$FeSi${}_2$O${}_7$

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