Abstract

Magnetic skyrmions are whirls of spin moments featuring a topological charge and a well-define topological charge density. In this talk, we show that the topological charge and the associated dipole moment are constants of motion, owing to the interplay between the skyrmion's topology and the translational invariance. As a result, skyrmions are intrinsically pinned to be completely immobile, analogous to fractons--exotic quasiparticles first discovered in quantum spin models and obeying similar mobility restriction as well as conservation of multipolar moments of their U(1) charge. We propose skyrmion-hosting systems as a promising platform for exploring fractonic phenomena experimentally, which remains rather unexplored due to the scarcity of realistic systems that host fractons. Also, using a linear spin-wave theory, we elucidate that the immobility of the skyrmion is the result of a perfect cancellation between the complex dynamics of the classical spin texture and that of a cloud of quantum magnons. Moreover, the conservation laws are intimately linked with the feature that the topological charge density is a generator of area-preserved diffeormophism. We find that the topological charge density obeys the Girvin-MacDonald-Platzman algebra, which governs the charge neutral excitations in fractional quantum Hall systems. This strongly suggests an exciting prospect for exploring bosonic fractional quantum Hall physics in systems of strongly interacting skyrmions.

Reference
[1] Topological dipoles of quantum skyrmions, S.Sorn, J.Schmalian, M.Garst, arXiv:2412:16284 (2024).