N K Pi molecular state with I=1 and J(Pi)=3/2-

The structure of the molecule-like state of $NK\pi$ with spin-parity $J^{\pi}={3/2}^-$ and isospin I=1 is studied within the chiral SU(3) quark model. First we calculate the $NK$, $N\pi$, and $K\pi$ phase shifts in the framework of the resonating group method (RGM), and a qualitative agreement with the experimental data is obtained. Then we perform a rough estimation for the energy of $(NK\pi)_{J^{\pi}={3/2}^-,I=1}$, and the effect of the mixing to the configuration $(\Delta K)_{J^{\pi}={3/2}^-,I=1}$ is also considered. The calculated energy is very close to the threshold of the $NK\pi$ system. A detailed investigation is worth doing in the further study.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Tunneling-induced restoration of classical degeneracy in quantum kagome ice

Quantum effect is expected to dictate the behavior of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a Z(2) topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasidegeneracy of states and effectively, the classical degeneracy is restored

Open-closed field algebras

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde