arXiv subjects
Publications and source records attributed to Stanislaw Walcerz.
In this lecture some mathematical tools necessary for a proper description of the Heisenberg antiferromagnet are presented. We would like to point out differences between ferro- and antiferromagnetic cases of Heisenberg Hamiltonian for finite spin systems. The ground-state properties are discussed.
Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary conditions one has to be very careful since the first gauge leads to a factor system which is not normalized. A period N introduced in Brown's and Zak's papers should be considered as a magnetic one, whereas the crystal period is in fact 2N. The `normalization' procedure proposed here shows the equivalence of Brown's, Zak's, and other approaches. It also indicates the importance of the concept of magnetic cells. Moreover, it is shown that factor systems (of projective representations and central extensions) are gauge-dependent, whereas a commutator of two magnetic translations is gauge-independent. This result indicates that a form of the vector potential (a gauge) is also important in physical investigations.