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      Electronic and phonon excitations in \(\alpha -\mathrm{RuC}{\mathrm{l}}_{3}\)

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          Anyons in an exactly solved model and beyond

           Alexei Kitaev (2005)
          A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static \(\mathbb{Z}_{2}\) gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number \(\nu\). The Abelian and non-Abelian phases of the original model correspond to \(\nu=0\) and \(\nu=\pm 1\), respectively. The anyonic properties of excitation depend on \(\nu\bmod 16\), whereas \(\nu\) itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
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            Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice materialNa2IrO3

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              Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

              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 Sr\(_2\)IrO\(_4\).
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                Author and article information

                Journal
                PRBMDO
                Physical Review B
                Phys. Rev. B
                American Physical Society (APS)
                2469-9950
                2469-9969
                October 2017
                October 11 2017
                : 96
                : 16
                Article
                10.1103/PhysRevB.96.165120
                © 2017
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