磁性Skyrmions是二维磁性材料中的准磁单极子
Magnetic Skyrmions are Quasi-Magnetic Monopoles in Two-Dimensional Magnetic Materials
摘要：
利用密度算符$ρ$的$su(N)$ Cartan子代数局部基参数化，证明了一般$N$能级量子系统的Wu-Yang势完全可用$SU(N)$规范变换表示.以$SU(2)$ Cartan子代数局部基作为局部归一化磁化矢量，发现磁skyrmion和吴杨磁skyrmion具有相同的代数结构.此外，将磁化强度的绝热幺正演化作为局域规范变换，证明了磁skyrmion的Wu-Yang势与Berry联系成正比，即磁skyrmion是准磁skyrmion.在一般$SU(N)$情形下，详细讨论了Wu-Yang势与Berry联系的精确关系，即纯态或混合态的Berry联系是$(N-1)$ Wu-Yang势的加权平均.
英文摘要：
Using $su(N)$ Cartan subalgebra local bases parametrization of density operator $ρ$, we prove that the Wu-Yang potentials of a general $N$-level quantum system are completely expressed by $SU(N)$ gauge transformation. By taking the $SU(2)$ Cartan subalgebra local basis as a local normalized magnetization vector, we find that magnetic skyrmion and Wu-Yang magnetic monopole have the same algebraic structure. Moreover, by taking the adiabatic unitary evolution of magnetization as local gauge transformation, we verify that the Wu-Yang potential of magnetic skyrmions is proportional to the Berry connection, this means that magnetic skyrmion is quasi-magnetic monopole. The exact relation between Wu-Yang potentials and Berry connection is discussed in detail for the general $SU(N)$ case, i.e. the Berry connection for the pure or mixed state is the weighted average of the $(N-1)$ Wu-Yang potentials.
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