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      Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

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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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            Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4.

            B. Kim, H Ohsumi, T Komesu … (2009)
            Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent atomic orbitals in an electronic wave function, which uncovers the unconventional Mott insulating state induced by relativistic spin-orbit coupling in the layered 5d transition metal oxide Sr2IrO4. A selection rule based on intra-atomic interference effects establishes a complex spin-orbital state represented by an effective total angular momentum = 1/2 quantum number, the phase of which can lead to a quantum topological state of matter.
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              Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice materialNa2IrO3

              Yogesh Singh, P Gegenwart (2010)
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                Author and article information

                Journal
                Title: Nature Physics
                Abbreviated Title: Nat Phys
                Publisher: Springer Nature
                ISSN (Print): 1745-2473
                ISSN (Electronic): 1745-2481
                Publication date Created: May 11 2015
                Publication date (Print): May 11 2015
                Volume: 11
                Issue: 6
                Pages: 462-466
                Article
                DOI: 10.1038/nphys3322
                SO-VID: a491f9b5-4118-4410-ba4d-d7e3bcaa6b53
                Copyright © © 2015
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