Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding

In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is directly related to global transformations of the ground-state wavefunctions on a torus (the modular transformations). On the other hand, there are theoretical descriptions of various topologically ordered states in 3+1D, which exhibit both point-like and loop-like excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of loop-like excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a non-trivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work we consider realizations of topological order in 3+1D using cohomological gauge theory in which the loops have Abelian statistics, and explicitly demonstrate our results on examples with $Z_2\times Z_2$ topological order

Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice

Recently two interesting candidate quantum phases --- the chiral spin density wave state featuring anomalous quantum Hall effect and the d+id superconductor --- were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and t-J model on the honeycomb lattice at 1/4-doping. The main advantage of our approach is the use of symmetry quantum numbers of ground state wavefunctions on finite size systems (up to 32 sites) to sharply distinguish different quantum phases. Our results show that for $1\lesssim U/t< 40$ in the Hubbard model and for $0.1< J/t<0.80(2)$ in the t-J model, the quantum ground state is either a chiral spin density wave state or a spin-charge-Chern liquid, but not a d+id superconductor. However, in the t-J model, upon increasing $J$ the system goes through a first-order phase transition at $J/t=0.80(2)$ into the d+id superconductor. Here the spin-charge-Chern liquid state is a new type of topologically ordered quantum phase with Abelian anyons and fractionalized excitations. Experimental signatures of these quantum phases, such as tunneling conductance, are calculated. These results are discussed in the context of 1/4-doped graphene systems and other correlated electronic materials on the honeycomb lattice.Comment: Some parts of text revised for clarity of presentatio

Studies on Improving the Regioselectivity of Reactions of Sucrose: The Role of Molecular Recognition and Polymer Supported Syntheses

The world economy is critically dependent upon natural resources. Because sucrose can be inexpensively produced in large quantities and refined to a purity unequalled by almost all other natural products, it has been exploited as an industrial raw material for many years, primarily as a sweetener. A major difficulty in utilizing sucrose as an industrial feedstock is the lack of regioselectivity in synthetic reactions due to its eight hydroxyl groups of similar reactivity. The long range goal in this work is to apply the technique of molecular recognition by template imprinting to the creation of a material that will bind to sucrose and block certain of the hydroxyl groups. Sucrose is a disaccharide composed of D-fructose and D-glucose with the glucose in a chair conformation. The strategy is to use D-glucose as a template to synthesize a monomer with covalently bonded vinyl groups. The monomer would be copolymerized with another monomer and a crosslinking agent to prepare a three-dimensional polymer, incorporating the glucose template. Removal of the glucose would leave a cavity with the same conformation as the glucose part of the sucrose molecule. Sucrose should then bind to the polymer cavity. This method could increase the regioselectivity of reactions of sucrose by blocking the glucose end of sucrose to permit reactions to occur on the fructose portion. Alternatively, a reaction could occur within the cavity. The stereochemistry of the functional groups inside the cavity would be primarily responsible for the molecular recognition characteristics of the cavity. Methyl 2,3,4,6-tetra-O-methacryloyl-α-D-glucopyranoside, 4-nitrophenyl 2,3,4,6-tetra-O-methacryloyl-α-D-glucopyranoside, and 4-nitrophenyl 2,3,4,6-tetra-O-methacryloyl-β-D-glucopyranoside were chosen as possible monomers. These monomers have been synthesized and characterized by spectroscopy and elemental analysis. Copolymerization of these three monomers with styrene and divinylbenzene have been carried out by using azobisisobutryonitrile (AIBN) as the initiator. A high concentration of crosslinking agent (divinylbenzene 50% in reaction mixture) was present in the polymerization mixtures and three-dimensional polymers were formed with high rigidity. The polymers have been characterized by spectroscopy and other techniques

Spin pumping and spin-transfer torques in antiferromagnets

Spin pumping and spin-transfer torques are two reciprocal phenomena widely studied in ferromagnetic materials. However, pumping from antiferromagnets and its relation to current-induced torques have not been explored. By calculating how electrons scatter off a normal metal-antiferromagnetic interface, we derive pumped spin and staggered spin currents in terms of the staggered field, the magnetization, and their rates of change. For both compensated and uncompensated interfaces, spin pumping is of a similar magnitude as in ferromagnets with a direction controlled by the polarization of the driving microwave. The pumped currents are connected to current-induced torques via Onsager reciprocity relations.Comment: 5 pages, 4 figure

Studies on Improving the Regioselectivity of Reactions of Sucrose: The Role of Molecular Recognition and Polymer Supported Syntheses

The world economy is critically dependent upon natural resources. Because sucrose can be inexpensively produced in large quantities and refined to a purity unequalled by almost all other natural products, it has been exploited as an industrial raw material for many years, primarily as a sweetener. A major difficulty in utilizing sucrose as an industrial feedstock is the lack of regioselectivity in synthetic reactions due to its eight hydroxyl groups of similar reactivity. The long range goal in this work is to apply the technique of molecular recognition by template imprinting to the creation of a material that will bind to sucrose and block certain of the hydroxyl groups. Sucrose is a disaccharide composed of D-fructose and D-glucose with the glucose in a chair conformation. The strategy is to use D-glucose as a template to synthesize a monomer with covalently bonded vinyl groups. The monomer would be copolymerized with another monomer and a crosslinking agent to prepare a three-dimensional polymer, incorporating the glucose template. Removal of the glucose would leave a cavity with the same conformation as the glucose part of the sucrose molecule. Sucrose should then bind to the polymer cavity. This method could increase the regioselectivity of reactions of sucrose by blocking the glucose end of sucrose to permit reactions to occur on the fructose portion. Alternatively, a reaction could occur within the cavity. The stereochemistry of the functional groups inside the cavity would be primarily responsible for the molecular recognition characteristics of the cavity. Methyl 2,3,4,6-tetra-O-methacryloyl-α-D-glucopyranoside, 4-nitrophenyl 2,3,4,6-tetra-O-methacryloyl-α-D-glucopyranoside, and 4-nitrophenyl 2,3,4,6-tetra-O-methacryloyl-β-D-glucopyranoside were chosen as possible monomers. These monomers have been synthesized and characterized by spectroscopy and elemental analysis. Copolymerization of these three monomers with styrene and divinylbenzene have been carried out by using azobisisobutryonitrile (AIBN) as the initiator. A high concentration of crosslinking agent (divinylbenzene 50% in reaction mixture) was present in the polymerization mixtures and three-dimensional polymers were formed with high rigidity. The polymers have been characterized by spectroscopy and other techniques