Holographic coherent states from random tensor networks

Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We set up a framework in which all possible bulk spatial geometries, characterized by weighted adjacent matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded on this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update

Determinant Representation of Correlation Functions for the Uq(gl(1∣1))U_q(gl(1|1)) Free Fermion Model

With the help of the factorizing $F$-matrix, the scalar products of the $U_q(gl(1|1))$ free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.Comment: Latex File, 20 pages, V.3: some discussions are added, V.4 Reference update, this version will appear in J. Math. Phy

Drinfeld twists and algebraic Bethe ansatz of the supersymmetric model associated with Uq(gl(m∣n))U_q(gl(m|n))

We construct the Drinfeld twists (or factorizing $F$-matrices) of the supersymmetric model associated with quantum superalgebra $U_q(gl(m|n))$, and obtain the completely symmetric representations of the creation operators of the model in the $F$-basis provided by the $F$-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the $F$-basis for the $U_q(gl(2|1))$-model (the quantum t-J model).Comment: Latex file, 33 pages; V2: minor typos corrected;V3: Reference update, the new version will appear in Commun. Maths. Phys;V4: misprints correcte

3-{2-[(1,3-Benzothia­zol-2-yl)sulfanyl­meth­yl]phen­yl}-4-meth­oxy-5,5-dimethyl­furan-2(5H)-one

In the title compound, C21H19NO3S2, the dihedral angles formed between the thia­zole ring and the adjacent benzene ring and the other benzene ring are 1.58 (3) and 76.48 (6)°, respectively. The crystal structure features a weak C—H⋯O inter­action