Symmetry protected topological orders and the group cohomology of their symmetry group

Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain is the first example of SPT phase which is protected by SO(3) spin rotation symmetry. The topological insulator is another exam- ple of SPT phase which is protected by U(1) and time reversal symmetries. It has been shown that free fermion SPT phases can be systematically described by the K-theory. In this paper, we show that interacting bosonic SPT phases can be systematically described by group cohomology theory: distinct d-dimensional bosonic SPT phases with on-site symmetry G (which may contain anti-unitary time reversal symmetry) can be labeled by the elements in H^{1+d}[G, U_T(1)] - the Borel (1 + d)-group-cohomology classes of G over the G-module U_T(1). The boundary excitations of the non-trivial SPT phases are gapless or degenerate. Even more generally, we find that the different bosonic symmetry breaking short-range-entangled phases are labeled by the following three mathematical objects: (G_H, G_{\Psi}, H^{1+d}[G_{\Psi}, U_T(1)], where G_H is the symmetry group of the Hamiltonian and G_{\Psi} the symmetry group of the ground states.Comment: 55 pages, 42 figures, RevTeX4-1, included some new reference

Enchanced levels of apolipoprotein M during HBV infection feedback suppresses HBV replication

<p>Abstract</p> <p>Background</p> <p>Chronic liver diseases can interfere with hepatic metabolism of lipoproteins, apolipoproteins. Hepatitis B virus (HBV) is a major etiological agent causing acute and chronic liver diseases. Apolipoprotein M (ApoM) is a high-density lipoprotein (HDL) apolipoprotein and exclusively expressed in the liver parenchyma cells and in the tubular cells of the kidney. This study was to determine the correlation between HBV infection and ApoM expression.</p> <p>Materials and methods</p> <p>Serum ApoM levels in patients with HBV infection and in healthy individuals were measured by ELISA, ApoM mRNA expression were determined by RT-PCR, and the expression of S and E proteins of HBV, as well as the synthesis of viral DNA were measured by ELISA and real-time PCR.</p> <p>Results</p> <p>The levels of serum ApoM was significantly elevated in patients as compared to healthy individuals (<it>P </it>< 0.001), ApoM promoter activity, mRNA and protein expression were all stimulated in cells transfected with infectious HBV clone. In addition, ApoM decreases the expression of S and E proteins of HBV and the synthesis of viral DNA.</p> <p>Conclusion</p> <p>Raised ApoM levels in HBV infection may in turn suppress HBV replication, one of the protective mechanisms of nature.</p

Tensor product representation of topological ordered phase: necessary symmetry conditions

The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional methods due to their long range entanglement. However, an important issue arises when we use tensor product states (TPS) as variational states to find the ground state of a Hamiltonian: can arbitrary variations in the tensors that represent ground state of a Hamiltonian be induced by local perturbations to the Hamiltonian? Starting from a tensor product state which is the exact ground state of a Hamiltonian with $\mathbb{Z}_2$ topological order, we show that, surprisingly, not all variations of the tensors correspond to the variation of the ground state caused by local perturbations of the Hamiltonian. Even in the absence of any symmetry requirement of the perturbed Hamiltonian, one necessary condition for the variations of the tensors to be physical is that they respect certain $\mathbb{Z}_2$ symmetry. We support this claim by calculating explicitly the change in topological entanglement entropy with different variations in the tensors. This finding will provide important guidance to numerical variational study of topological phase and phase transitions. It is also a crucial step in using TPS to study universal properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure

Complete classification of 1D gapped quantum phases in interacting spin systems

Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D spin systems in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B \textbf{83}, 035107 (2011); arXiv:1008.3745]. It was found that, such symmetry protected topological (SPT) phases are labeled by the projective representations of the symmetry group which can be viewed as a symmetry fractionalization. In this paper, we extend the classification of 1D gapped phases by considering SPT phases with combined time reversal, parity, and/or on-site unitary symmetries and also the possibility of symmetry breaking. We clarify how symmetry fractionalizes with combined symmetries and also how symmetry fractionalization coexists with symmetry breaking. In this way, we obtain a complete classification of gapped quantum phases in 1D spin systems. We find that in general, symmetry fractionalization, symmetry breaking and long range entanglement(present in 2 or higher dimensions) represent three main mechanisms to generate a very rich set of gapped quantum phases. As an application of our classification, we study the possible SPT phases in 1D fermionic systems, which can be mapped to spin systems by Jordan-Wigner transformation.Comment: 15 pages, 3 figure

A revisit of superconductivity in 4HbH_b-TaS2−2x_{2-2x}Se2x_{2x} single crystals

Previous investigations of 4$H_b$-TaS$_{2-2x}$Se$_{2x}$ mainly focused on the direct competition between superconductivity and charge density wave (CDW). However, the superconductivity itself, although has been prominently enhanced by isovalent Se substitution, has not been adequately investigated. Here, we performed a detailed electrical transport measurement down to 0.1 K on a series of 4$H_b$-TaS$_{2-2x}$Se$_{2x}$ single crystals. A systematic fitting of the temperature-dependent resistance demonstrates that the decreased Debye temperatures ($\Theta_{D}$) and higher electron-phonon coupling constants ($\lambda_{e-p}$) at the optimal Se doping content raise the superconducting transition temperature ($T_c$). Additionally, we discovered that the incorporation of Se diminishes the degree of anisotropy of the superconductivity in the highly layered structure. More prominently, a comprehensive analysis of the vortex liquid phase region reveals that the optimally doped sample deviates from the canonical 2D Tinkham prediction but favors a linear trend with the variation of the external magnetic field. These findings emphasize the importance of interlayer interaction in this segregated superconducting-Mott-insulating system.Comment: 11 pages, 5 figure

Prediction and Study of Air Thermal Parameters in Unexploited Mine Regions Based on Temperature Prediction Model in Whole Ventilation Network

AbstractMines with heat disaster danger have been increased year by year, in order to provide basic data for mine air- conditioning design, prediction of air thermal parameters in the mine unexploited region becomes particularly important. But at present, prediction of air thermal parameters is realized mainly by empirical formula and forecast method of single-line(main trunk road method), existing many disadvantages such as strong individual subjectivity, bad theoretical property and low forecasting precision. Therefore, a kind of air temperature prediction model in whole ventilation network based on wind enthalpy equation is put forward. By the model, air temperature prediction software in whole ventilation network which can make reasonable forecast of thermal parameters for different high temperature mines is programmed by determining air thermal parameters through wind energy equation and considering the influence of natural wind pressure. Through the prediction of the air thermal parameters of the wind route in the fifth mining area in east wing of Dongtan colliery, it can be seen that air temperature prediction model in whole ventilation network is scientific, reasonable and with strong operating nature, which can meet the requirements of the prediction of air thermal parameters in unexploited region of high temperature mines

Certain Class of Analytic Functions Based on qq-difference operator

In this paper, we considered a generalized class of starlike functions defined by Kanas and R\u{a}ducanu\cite{10} to obtain integral means inequalities and subordination results. Further, we obtain the for various subclasses of starlike functions.Comment: