Langevin dynamics of generalized spins as SU($N$) coherent states

Abstract

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude $S$ have $N=2S+1$ levels. Alternatively, the spin state is fully characterized by a set of $N^2-1$ local physical observables, which we interpret as generalized spin components. For example, a spin with $S=1$ has three dipole components and five quadrupole components. These components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU($N$) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a non-equilibrium relaxation process that creates CP${}^2$ Skyrmions, which are topological defects with both dipole and quadrupole character.

References in corpus (17)

• A method for atomistic spin dynamics simulations: implementation and examples
• Magnetic Field-Induced Condensation of Triplons in Han Purple Pigment BaCuSi${}_2$O${}_6$
• Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions
• Bose-Einstein Condensation of S = 1 Ni spin degrees of freedom in NiCl2-4SC(NH2)2
• Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
• Stable and fast semi-implicit integration of the stochastic Landau-Lifshitz equation
• Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi${}_2$F${}_7$
• Hybridized quadrupolar excitations in the spin-anisotropic frustrated magnet FeI2
• Generalized spin-wave theory: application to the bilinear-biquadratic model
• Classical spin dynamics based on SU($N$) coherent states
• Noise and dissipation on coadjoint orbits
• Geometric integration of classical spin dynamics via a mean-field Schrödinger equation
• Lie-Poisson methods for isospectral flows
• Semi-classical simulation of spin-1 magnets
• Symplectic integrators for spin systems
• Decay and renormalization of a longitudinal mode in a quasi-two-dimensional antiferromagnet
• Collective Lie-Poisson integrators on ${\mathbf{R}}^3$

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