We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1 + 1)dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c < 1. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but non-zero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, non-chiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the ten-fold way classification of two-dimensional non-interacting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist. arXiv:1601.01094v2 [cond-mat.str-el]

Novel Raman tags called nanoaggregate‐embedded beads (NAEBs) have been developed. NAEBs are silica‐coated, dye‐induced aggregates of a small number of metal nanoparticles. In this work, the Raman reporters used to induce aggregation of gold nanoparticles include strongly binding dyes such as XRITC, TRITC, and DTDC and weakly binding dyes such as R6G. Surface‐enhanced Raman scattering (SERS) signal from a single NAEB can be detected. This study also demonstrates that these SERS‐active beads can be used as Raman tags for bio‐detection.

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Colorful palette: A new class of highly selective Eu3+‐based multi‐frequency PARACEST agents is reported. The complexes can be tuned when administered simultaneously thereby allowing for the possibility of monitoring multiple biomarkers in parallel. PARACEST = paramagnetic chemical exchange saturation transfer.

We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with SU (2)-symmetric spin-spin interactions. The two-leg ladders are then arranged on rows and coupled through SU (2)-symmetric interactions between consecutive ladders. The intraladder interactions are tuned so as to realize the c = 1/2 Ising conformal field theory, a fact that we establish numerically via Density Matrix Renormalization Group (DMRG) studies. Time-reversal breaking inter-ladder interactions are tuned so as to open a bulk gap in the 2D lattice system. This 2D system supports gapless chiral edge modes with Ising non-Abelian excitations but no charge excitations, in contrast to the Pfaffian non-Abelian fractional quantum Hall state.That point particles may obey non-Abelian braiding statistics in (2+1)-dimensional spacetime has been known in quantum-field theory since the 1980's [1][2][3][4][5]. Moore and Read showed in 1991 that certain Pfaffian wave functions support quasi-particles with non-Abelian braiding statistics [6]. This discovery opened the possibility that non-Abelian braiding statistics could be found in certain fractional quantum Hall plateaus [6][7][8][9].A second physical platform to realize braiding statistics that is neither bosonic nor fermionic is provided by quasitwo-dimensional quantum spin magnets with a gapped chiral spin-liquid ground state [10, 11]. Quasi-twodimensional arrays of quantum spin chains also have the potential for realizing gapped spin liquid ground states with quasi-particles obeying Abelian or non-Abelian braiding statistics [12][13][14][15].In this paper, we construct a two-dimensional (2D) lattice model, depicted in Fig. 1, that is argued to realize a non-Abelian chiral spin liquid. This 2D model consists of an array of coupled one-dimensional (1D) two-leg quantum spin-1/2 ladders. The inter-ladder coupling leads to a bulk gap, while gapless modes remain at the boundaries. The chiral edge states correspond to the Ising conformal field theory (CFT) with central charge c = 1/2, similarly to the Moore-Read Pfaffian state. However, in contrast to the Pfaffian quantum Hall state, there is no additional c = 1 chiral bosonic charge-carrying edge mode. By the bulk-edge correspondence, the bulk of the coupled spin-ladder model is a gapped chiral spin liquid supporting Ising non-Abelian topological order [16,17].To obtain this result, we argue that the aforementioned lattice model is a regularization of one of the interacting quantum-field theories presented in Ref. 14, one that supports chiral non-Abelian topological order. We start from coupled two-leg ladders (called bundles in Ref. 14), on which sites quantum spin-1/2 degrees of freedom are localized. Two ingredients are needed. First, the interactions within the two-leg ladders should be fine-tuned so as to realize the Ising universality class in (1+1)-dimensional spacetime, the Ising criticality in short. Second, the...