Abstract
To investigate the emergent quantum phases and topologies, we explore both conventional SU(2) spin and more generic SU(N) spin systems. In the large-S limit, we focus on the formation and manipulation of magnetic skyrmions and propose two distinct schemes based on the Dzyaloshinskii-Moriya interaction. The first one is realized with a multiferroic van der Waals heterostructure, in which both ab initio and Ginzburg-Landau analysis indicate an efficient engineering channel to write/delete magnetic skyrmions via electric fields. For the other scheme we consider the interplay between classical spins and itinerant electrons by doping magnetic atoms on the surface of a three-dimensional topological insulator. Utilizing the same methods, we find that noncollinear spin textures, including the spin spirals and the skyrmion lattice, can be induced by Dirac electrons. Further studies on the feedback effect show that the behavior of Dirac electrons is drastically changed by the magnetic coupling.
Going beyond the conventional SU(2) spins by augmenting the symmetry group to SU(N), quantum fluctuations would be strongly enhanced but can still be harnessed in the large-N limit. We intertwine the SU(N) symmetry and frustration on both honeycomb and triangular antiferromagnets and integrate them through tuning the J1-J2 Heisenberg interactions. Through a superior minimization algorithm with the self-consistency and strict local constraints, a plethora of quantum states is identified and discussed, including the Dirac spin liquid, chiral spin liquids, and various confined symmetry-breaking states. It is expected these results can stimulate further studies on SU(N) physics, especially in the ultracold-atom systems, and facilitate the understanding of the approximate physics in solid-state materials such as twisted moiré systems.
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