标题： 二维自旋-1/2系统的Skyrmion族 显示英文标题

标题： Families of Skyrmions in Two-Dimensional Spin-1/2 Systems

摘要： 我们发现二维自旋-1/2系统中存在类似Skyrmion的拓扑激发。 将自旋波函数表示为旋转算符，可将自旋-1/2系统映射到Manakov系统。 我们采用解析和数值方法来求解得到的Manakov系统。 通过广义相似性变换，我们将二维Manakov系统简化为可积的一维Manakov系统。 以这种方式获得的解在原点发散。 我们采用幂级数方法获得一个由有限数量节点表征的局部化且不发散的解的无限族。 然后使用数值方法获得一个由无限数量节点对应的局部化振荡解族，这些解对应于由同心环组成的Skyrmion，其两个自旋分量的强度交替变化。 我们通过根据其有效尺寸计算能量泛函来研究此处找到的Skyrmion解的稳定性。 结果表明，当同心环之间的相位差为$\pi$时，即自旋向上和自旋向下交替时，Skyrmion最稳定。 我们的结果也适用于双极化光学脉冲。 显示英文摘要

摘要： We find Skyrmion-like topological excitations for a two-dimensional spin-1/2 system. Expressing the spinor wavefunction in terms of a rotation operator maps the spin-1/2 system to a Manakov system. We employ both analytical and numerical methods to solve the resulting Manakov system. Using a generalized similarity transformation, we reduce the two-dimensional Manakov system to the integrable one-dimensional Manakov system. Solutions obtained in this manner diverge at the origin. We employ a power series method to obtain an infinite family of localized and nondiverging solutions characterized by a finite number of nodes. A numerical method is then used to obtain a family of localized oscillatory solutions with an infinite number of nodes corresponding to a skyrmion composed of concentric rings with intensities alternating between the two components of the spinor. We investigate the stability of the skyrmion solutions found here by calculating their energy functional in terms of their effective size. It turns out that indeed the skyrmion is most stable when the phase difference between the concentric rings is $\pi$, i.e., alternating between spin up and spin down. Our results are also applicable to doubly polarized optical pulses.