Spin flux and magnetic solitons in an interacting two-dimensional electron gas: Topology of two-valued wave functions

For a topological antiferromagnet on a square lattice, with the standard Hartree-Fock, spin-density-wave decoupling of the on-site Hubbard interaction, there is an exact mapping of the low-energy one-electron excitation spectrum to a relativistic Dirac continuum field theory. In this field theory, the Dirac mass gap is precisely the Mott-Hubbard charge gap and the continuum field variable is an eight-component Dirac spinor describing the components of physical electron-spin amplitude on each of the four sites of the elementary plaquette in the original Hubbard model. Within this continuum model we derive explicitly the existence of hedgehog Skyrmion textures as local minima of the classical magnetic energy. These magnetic solitons carry a topological winding number [mu] associated with the vortex rotation of the background magnetic moment field by a phase angle 2[pi][mu] along a path encircling the soliton. Such solitons also carry a spin flux of [mu][pi] through the plaquette on which they are centered. The [mu]=1 hedgehog Skyrmion describes a local transition from the topological (antiperiodic) sector of the one-electron Hilbert space to the nontopological sector. We derive from first principles the existence of deep level localized electronic states within the Mott-Hubbard charge gap for the [mu]=1 and 2 solitons. The spectrum of localized states is symmetric about [ital E]=0 and each subgap electronic level can be occupied by a pair of electrons in which one electron resides primarily on one sublattice and the second electron on the other sublattice. It is suggested that flux-carrying solitons and the subgap electronic structure which they induce are important in understanding the physical behavior of doped Mott insulators.