Spin model

Abstract: We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

Abstract: Skyrmions are topologically protected field configurations with particle-like properties that play an important role in various fields of science. Recently, skyrmions have been observed to be stabilized by an external magnetic field in bulk magnets. Here, we describe a two-dimensional square lattice of skyrmions on the atomic length scale as the magnetic ground state of a hexagonal Fe film of one-atomic-layer thickness on the Ir(111) surface. Using spin-polarized scanning tunnelling microscopy we can directly image this non-collinear spin texture in real space on the atomic scale and demonstrate that it is incommensurate to the underlying atomic lattice. With the aid of first-principles calculations, we develop a spin model on a discrete lattice that identifies the interplay of Heisenberg exchange, the four-spin and the Dzyaloshinskii-Moriya interaction as the microscopic origin of this magnetic state.

Abstract: We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a finite-dimensional vector space. These states can be considered as generalized valence bond states, and they are dense in the set of all translation invariant states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic “Neel ordered” states. The ergodic components have exponential decay of correlations. All states considered can be obtained as “local functions” of states of a special kind, so-called “purely generated states,” which are shown to be ground states for suitably chosen finite range VBS interactions. We show that all these generalized VBS models have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group. In particular we illustrate our results with a one-parameter family of examples which are not isotropic except for one special case. This isotropic model coincides with the one-dimensional antiferromagnet, recently studied by Affleck, Kennedy, Lieb, and Tasaki.