Magnetic Skyrmions are Quasi-Magnetic Monopoles in Two-Dimensional Magnetic Materials

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.