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

David Dahlbom, Cole Miles, Hao Zhang, Cristian D. Batista, Kipton Barros

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16 Scopus citations

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 N2-1 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 nonequilibrium relaxation process that creates CP2 skyrmions, which are topological defects with both dipole and quadrupole character.

Original languageEnglish
Article number235154
JournalPhysical Review B
Volume106
Issue number23
DOIs
StatePublished - Dec 15 2022
Externally publishedYes

Funding

The authors thank Shi-Zeng Lin and Leandro Chinellato for helpful discussions. D.D. and C.D.B. acknowledge support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC-0018660. This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. K.B. acknowledges support from the Center of Materials Theory as a part of the Computational Materials Science (CMS) program, funded by the U.S. Department of Energy, Office of Basic Energy Sciences.

FundersFunder number
National Science FoundationPHY-1607611
U.S. Department of Energy
Office of Science
Basic Energy SciencesDE-SC-0018660

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