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We derive from first principles the existence of deep level localized electronic gap states, induced by hedgehog solitons, in the two-dimensional Hubbard model. These arise naturally as excitations in a new topological magnetic condensate of the many-electron system associated with 7Ti(SO (3)). The condensate exhibits local spin | magnetic moments as well as topological "spin flux." This flux emerges microscopically from a homotopically nontrivial phase rotation of the electron spinor field and leads to an intriguing relativistic structure for the Mott-Hubbard gap.PACS numbers: 71.27.+a, 74.20.Hi, 75.30.Fv The discovery of high temperature superconductivity [1] has sparked broad interest in the magnetic properties of strongly correlated electron systems. It was suggested by Anderson [2] that a spin-liquid phase of strongly interacting electrons may be responsible for many of the anomalous electronic and magnetic features observed in such systems [3]. In this paper we describe a new topological feature of the interacting electronic system in two dimensions which may give rise to such anomalies.In a recent series of papers [4-6], we have presented a careful study of the magnetic and electronic properties of the strongly correlated Hubbard model starting from a mean field theory of spiral magnetism and continuing to the lowest order fluctuation corrections. The fluctuation Hamiltonian led to a physical picture of the doped Mott-Hubbard system as a highly nontrivial metal in which there was strong coupling between collective charge and spin excitations. The aim of this study was to isolate those normal state properties of the copperoxide high temperature superconductors which may be associated with small fluctuations about a spiral magnetic mean field, from those which require large amplitude nonlinear corrections or an entirely new condensate at the mean field level. We found that certain features such as the twist of the magnetic background, the closure of the Mott-Hubbard gap [4,5], and the sign change of the Hall coefficient [6] with doping 6 could be described in standard spin-density-wave mean field theory of the intermediate coupling Hubbard model. However, other important features such as the rapid loss of magnetic long range order with <5, the marginal Fermi-liquid behavior [7], and the striking mid-infrared absorption [8] could not be accounted for in a natural way.In this paper we discuss the properties of a topological fluctuation correction which connects the previous mean field ground state to a possible new condensate at large doping. Unlike the standard spiral magnetic states, the many-electron wave function for this topological condensate is a Slater determinant of single electron spinor wave functions in coordinate space which change sign under 2n rotation about an axis z, passing through the center of any lattice plaquette. These single electron states are obtained by applying a homotopically nontrivial phase rotation to the electron spin for paths that encircle an elementary plaquette of the 2D...

We demonstrate from first principles that ferromagnetic core, meron vortex configurations of the spin-1 2 antiferromagnet in two-dimensions give rise to midgap electronic states in the Mott-Hubbard charge gap. Merons are collective mode excitations of the antiferromagnet and are induced by doping the system with charge carriers. They are the topological analogs of charged bosonic domain wall solitons in one-dimension.

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