A Schrödinger Formulation of Generalized Landau-Lifshitz Dynamics: Numerical Techniques and Applications

The Landau-Lifshitz (LL) equations may be derived using the formalism of SU(2) coherent states. For many spin systems, such as those possessing strong onsite anisotropy and spin greater than ½, it is more appropriate to take a classical limit based on coherent states of SU(N), where N > 2. The resulting generalization of the LL equations are naturally derived in the Heisenberg picture, setting up a correspondence between quantum observables and classical variables. We show that one may instead develop an equivalent Schrödinger dynamics directly on coherent states. This formulation involves fewer variables than the Heisenberg approach and possesses a global Hamiltonian structure. The latter fact enables the application of energy-preserving geometric integration schemes. The dynamics may also be coupled to a thermal bath, resulting in a generalization of the stochastic LL equations. Sunny, a software package for simulating spin systems using SU(N) coherent states, has been developed to make these theoretical advancements accessible. Examples are provided, including a physically realistic spin one Hamiltonian that supports both a novel type of skyrmion crystal at low temperatures as well as a metastable skyrmion gas state, the density of which is controlled by quenching rate.