Possibility of S=1 spin liquids with fermionic spinons on triangular lattices

In this paper we generalize the fermionic representation for $S=1/2$ spins to arbitrary spins. Within a mean field theory we obtain several spin liquid states for spin $S=1$ antiferromagnets on triangular lattices, including gapless f-wave spin liquid and topologically nontrivial $p_x+ip_y$ spin liquid. After considering different competing orders, we construct a phase diagram for the $J_1$-$J_3$-$K$ model. The application to recently discovered material $\mathrm{NiGa_2S_4}$ is discussed.Comment: 5 pages, 3 figure

Spinor Decomposition of SU(2) Gauge Potential and The Spinor Structures of Chern-Simons and Chern Density

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor structures, the knot quantum number of non-Abelian gauge theory is discussed, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping.Comment: 11 page

Fermionic theory for quantum antiferromagnets with spin S > 1/2

The fermion representation for S = 1/2 spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of S =1/2 fermion representation is absent for S > 1/2. As a result, different path integral representations and mean field theories can be formulated for spin models. In particular, we construct a Lagrangian with restored particle-hole symmetry, and apply the corresponding mean field theory to one dimensional (1D) S = 1 and S = 3/2 antiferromagnetic Heisenberg models, with results that agree with Haldane's conjecture. For a S = 1 open chain, we show that Majorana fermion edge states exist in our mean field theory. The generalization to spins with arbitrary magnitude S is discussed. Our approach can be applied to higher dimensional spin systems. As an example, we study the geometrically frustrated S = 1 AFM on triangular lattice. Two spin liquids with different pairing symmetries are discussed: the gapped px + ipy-wave spin liquid and the gapless f-wave spin liquid. We compare our mean field result with the experiment on NiGa2S4, which remains disordered at low temperature and was proposed to be in a spin liquid state. Our fermionic mean field theory provide a framework to study S > 1/2 spin liquids with fermionic spinon excitations.Comment: 16 pages, 4 figure

Genetic incorporation of D-Lysine into diketoreductase in Escherichia coli cells

D-Lysine has been genetically introduced into diketoreductase in E. coli cells by utilization of an orthogonal Ph tRNA /Lysyl-tRNA synthetase pair. This is the first report on the genetic incoporation of D-amino acids into proteins, which may be generally applicable to a wide variety of applications