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In this talk, we first introduce the gauge field induced by topological spin textures. We briefly review how this emergent gauge field leads to topological phenomena in magnetic skyrmions, which are microscopic magnetic vortices with an integer topological charge. We then consider topological spin textures in triangular lattice antiferromagnets, where the ground state has SO(3) symmetry, such as the 120-degree order and the four-sublattice tetrahedral order. The SO(3) order parameter is known to host a Z2 vortex as a topological defect. We present our recent work on the formation of the Z2 vortex crystal within the tetrahedral order [1]. We also discuss the possibility of fractional bound charges and their fractional statistics. In the second topic, we discuss quantum applications of topological defects with a focus on domain walls. Employing the density-matrix renormalization group method, we discuss the domain wall qubits and their single-qubit and two-qubit gate operations [2].

[1] “Z2 Vortex Crystals and Topological Magnons in a Tetrahedral Antiferromagnet”, T. Hirosawa, A. Mook, M. Azhar, arXiv:2503.06008.
[2] “Density Matrix Renormalization Group Study of Domain Wall Qubits”, G. Qu, J. Zou, D. Loss, and T. Hirosawa, arXiv:2412.11585.

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