Entanglement Spectra of the quantum hard-square model: Holographic minimal models

We study the entanglement properties of a quantum lattice-gas model for which we can find the exact ground state (of the Rokhsar-Kivelson type). The ground state can be expressed as a superposition of states, each of which is characterized by a particle configuration with nearest-neighbor exclusion. We show that the reduced density matrix of the model on a ladder is intimately related to the transfer matrix of the classical hard-square model. The entanglement spectra of the model on square and triangular ladders are critical when parameters are chosen so that the corresponding classical hard-square models are critical. A detailed analysis reveals that the critical theories for the entanglement Hamiltonians are $c<1$ minimal conformal field theories. We further show that the entanglement Hamiltonian for the triangular ladder is integrable despite the fact that the original quantum lattice-gas model is non-integrable.Comment: 10 pages, 8 figure

Exact Analysis of Entanglement in Gapped Quantum Spin Chains

We investigate the entanglement properties of the valence-bond-solid states with generic integer-spin $S$. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, $2 \log_2 (S+1)$, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose a novel application of the edge state as a qubit for quantum computation.Comment: 4 pages, 2 figure

ZQZ_Q Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices

Adiabatic $Z_Q$ invariants by quantized Berry phases are defined for gapped electronic systems in $d$-dimensions ($Q=d+1$). This series includes Polyacetylene, Kagome and Pyrochlore lattice respectively for $d=1,2$ and 3. The invariants are quantum $Q$-multimer order parameters to characterize the topological phase transitions by the multimerization. This fractional quantization is protected by the global $Z_Q$ equivalence. As for the chiral symmetric case, a topological form of the $Z_2$-invariant is explicitly given as well.Comment: 4 pgages, 4 figure

Exact supersymmetry in the relativistic hydrogen atom in general dimensions -- supercharge and the generalized Johnson-Lippmann operator

A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact N = 2 supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2))in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.Comment: 4 pages, 1 figur

On the magic square C*-algebra of size 4

In this paper, we investigate the structure of the magic square C*-algebra (4) of size 4. We show that a certain twisted crossed product of (4) is isomorphic to the homogeneous C*-algebra 4 ( ($\mathbb{R}$$^3$)). Using this result, we show that (4) is isomorphic to the fixed point algebra of 4 ( ($\mathbb{R}$$^3$)) by a certain action. From this concrete realization of (4), we compute the K-groups of (4) and their generators

Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are $S=1,2$ dimerized Heisenberg chains and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.

Thermal performance analysis of a new structured-core translucent vacuuminsulation panel in comparison to vacuum glazing: Experimental and theoretically validated analyses

The notion at which, nowadays, building sector is being recognized to be nearly zero-energy buildings (NZEBs) relies partly on the thermal performance of its fabric insulation. Vacuum glazing (VG) technology attracted the research interest as an option to reduce heat loss through windows. However, the total glazing thermal transmittance (U-value) for VG increases with the use of smaller glazing area due to the edge-seal effects, due to the thermal short-circuit around the edges and the overall construction cost of VG leading to an unaffordable option to deal with energy conservation of buildings. Therefore, this study aims to propose a new structured core transparent vacuum insulation panel (TVIP) to accomplish insulation for the windows without edge sealing effect, with lower cost and can be easily retrofitted to the conventional windows of the existing buildings. To do this, VG and TVIP were constructed and their thermal conductivity were measured using heat flow meter apparatus. In addition, a 3D finite volume model considering the effect of surface to surface radiation, gas conduction, and thermal bridges through the spacer material and sealing material is developed. The model is validated with the experiments in this work and with the data for VG in the literature. The effect of vacuum pressure increase is simulated to mimic the vacuum deterioration problem and the effect of glazing size on the insulation performance of both VG and TVIP were investigated. The results indicate that for a smaller glazing area of less than 30 cm × 30 cm, the TVIP accomplished lower U-value compared with the VG at vacuum pressure of 0.1 Pa and 1 Pa. While, at a vacuum pressure of 10 Pa, the TVIP attained a lower U-value over the entire range of the investigated glazing sizes. Further, the edge-seal effect in the VG is diminished with the use of TVIP. Furthermore, the material cost per unit area of the TVIP is three times less than the cost of VG at laboratory scale. The results of the current study can guide vacuum window designers and researchers to further enhance the performance of TVIP based window to compete for the VG in the markets

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic