Magnetization Process from Chern-Simons Theory and Its Application to SrCu2(BO3)2

In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successful, this approach leads to interesting results when applied to the 2D AF magnet SrCu 2 (BO 3 ) 2 .