Duality Argument for the Chiral-Nematic Phase of Planar Spins

A duality argument for the recently discovered chiral-nematic phase of the XY model in a triangular lattice is presented. We show that a new Ising variable naturally emerges in mapping the antiferromagnetic J1-J2 classical XY spin Hamiltonian onto an appropriate Villain model on a triangular lattice. The new variable is the chirality degree of freedom, which exists in addition to the usual vortex variables, in the dual picture. Elementary excitations and the associated phase transition of the Ising degrees of freedom are discussed in some detail.Comment: Published version(4 pages, 2 figures

Vector chiral states in low-dimensional quantum spin systems

A class of exact spin ground states with nonzero averages of vector spin chirality, $$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.Comment: 4 pages, 1 figur

Coupling of phonons and spin waves in triangular antiferromagnet

We investigate the influence of the spin-phonon coupling in the triangular antiferromagnet where the coupling is of the exchange-striction type. The magnon dispersion is shown to be modified significantly at wave vector (2pi,0) and its symmetry-related points, exhibiting a roton-like minimum and an eventual instability in the dispersion. Various correlation functions such as equal-time phonon correlation, spin-spin correlation, and local magnetization are calculated in the presence of the coupling.Comment: 6 pages, 5 figures; references added, minor text revisions, submitted to PR

Landau level states on a topological insulator thin film

We analyze the four-dimensional Hamiltonian proposed to describe the band structure of the single-Dirac-cone family of topological insulators in the presence of a uniform perpendicular magnetic field. Surface Landau level(LL) states appear, decoupled from the bulk levels and following the quantized energy dispersion of a purely two-dimensional surface Dirac Hamiltonian. A small hybridization gap splits the degeneracy of the central n=0 LL with dependence on the film thickness and the field strength that can be obtained analytically. Explicit calculation of the spin and charge densities show that surface LL states are localized within approximately one quintuple layer from the surface termination. Some new surface-bound LLs are shown to exist at a higher Landau level index.Comment: 8 pages, 4 figure

Orbital Dzyaloshinskii-Moriya Exchange Interaction

Superexchange calculation is performed for multi-orbital band models with broken inversion symmetry. Orbital-changing hopping terms allowed by the symmetry breaking electric field lead to a new kind of orbital exchange term closely resembling the Dzyaloshinskii-Moriya spin exchange. The final superexchange Hamiltonian in two dimensions is expressed in terms of Gell-Mann matrices that break down as three spin operators and five nematic (quadrupole) order operators. Mean-field phase diagram exhibits a rich structure including anti-ferro-orbital, ferro-orbital, and both single and multiple spiral-orbital phases. Superexchange calculation for spinful, two-orbital model also strongly suggests a robust chiral-orbital order in the ground state.Comment: 6 pages, 1 figur