Topological Quantum Dimers Emerging from Kitaev Spin Liquid Bilayer: Anyon Condensation Transition

We present a bilayer spin model that illuminates the mechanism of topological anyon condensation transition. Our model harbors two distinct topological phases, Kitaev spin liquid bilayer state and resonating valence bond (RVB) state connected by a continuous transition. We show that the transition occurs by anyon condensation, and the hardcore dimer constraint of the RVB state plays a role of the order parameter. This model study offers an intuitive picture for anyon condensation transition, and is broadly applicable to generic tri-coordinated lattices preserving the emergence of the RVB state from the Kitaev bilayer.Comment: 6 pages, 4 figures + supplemental materia

Signatures of spin-triplet excitations in optical conductivity of valence bond solids

We show that the optical responses below the Mott gap can be used to probe the spin-triplet excitations in valence bond solid (VBS) phases in Mott insulators. The optical conductivity in this regime arises due to the electronic polarization mechanism via virtual electron hopping processes. We apply this mechanism to the Hubbard model with spin-orbit couplings and/or the corresponding spin model with significant Dzyaloshinskii-Moriya (DM) interactions, and compute the optical conductivity of VBS states on both ideal and deformed Kagome lattices. In case of the deformed Kagome lattice, we study the antiferromagnet, Rb$_2$Cu$_3$SnF$_{12}$ with the pinwheel VBS state. In case of the ideal Kagome lattice, we explore the optical conductivity signatures of the spin-triplet excitations for three VBS states with (1) a 12-site unit cell, (2) a 36-site unit cell with six-fold rotation symmetry, and (3) a 36-site unit cell with three-fold rotation symmetry, respectively. We find that increasing the DM interactions generally leads to broad and smooth features in the optical conductivity with interesting experimental consequences. The optical conductivity reflects the features of the spin-triplet excitations that can be measured in future experiments.Comment: Updated with the published version. 24 pages and 8 figure

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet

Motivated by the recent neutron scattering experiment on Rb2Cu3SnF12 [Nat. Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriya interactions in a theoretical model for the magnetic structure of this material. Considering the valence bond solid ground state, which has a 12-site unit cell, we develop the bond operator mean-field theory. It is shown that the Dzyaloshinskii-Moriya interactions significantly modify the triplon dispersions around the Gamma point and cause a shift of the spin gap (the minimum triplon gap) position from the K to Gamma point in the first Brilloin zone. The spin gap is also evaluated in exact diagonalization studies on a 24-site cluster. We discuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactions in the bond operator framework. Moreover, the magnetization process under external magnetic fields is studied within the exact diagonalization and strong coupling expansion approaches. We find that the results of all above approaches are consistent with the experimental findings.Comment: 14 pages, 10 figures; typos corrected, and acknowledgements and references adde