Competing electronic orders on Kagome lattices at van Hove filling

The electronic orders in Hubbard models on a Kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short range interactions. With increasing on-site repulsion $U$, the system develops successively ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction $V$ alone (U=0), the system develops intra-unit-cell charge density wave order for small $V$, s-wave superconductivity for moderate $V$, and the charge density wave order appears again for even larger $V$. With both $U$ and $V$, we also find spin bond order and chiral $d_{x^2 - y^2} + i d_{xy}$ superconductivity in some particular regimes of the phase diagram. We find that the s-wave superconductivity is a result of charge density wave fluctuations and the squared logarithmic divergence in the pairing susceptibility. On the other hand, the d-wave superconductivity follows from bond order fluctuations that avoid the matrix element effect. The phase diagram is vastly different from that in honeycomb lattices because of the geometrical frustration in the Kagome lattice.Comment: 8 pages with 9 color figure

Research of the active reflector antenna using laser angle metrology system

Active reflector is one of the key technologies for constructing large telescopes, especially for the millimeter/sub-millimeter radio telescopes. This article introduces a new efficient laser angle metrology system for the active reflector antenna of the large radio telescopes, with a plenty of active reflector experiments mainly about the detecting precisions and the maintaining of the surface shape in real time, on the 65-meter radio telescope prototype constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT). The test results indicate that the accuracy of the surface shape segmenting and maintaining is up to micron dimension, and the time-response can be of the order of minutes. Therefore, it is proved to be workable for the sub-millimeter radio telescopes.Comment: 10 pages, 15 figure

A multi-step quantum algorithm for solving problems with a special structure

In classical computation, a problem can be solved in multiple steps where calculation results of an intermediate step can be copied and reused. While in quantum computation, it is difficult to realize a multi-step calculation because the no-cloning theorem forbids making copies of an unknown quantum state perfectly. Here we find a method to protect and reuse unknown quantum state that encodes the calculation results of an intermediate step through quantum entanglement, therefore circumventing the restriction of the no-cloning theorem. Based on this method, we propose a multi-step quantum algorithm for finding the ground state of a Hamiltonian. We apply this algorithm for solving problems with a special structure: there exist a sequence of finite number of intermediate Hamiltonians between an initial Hamiltonian and the problem Hamiltonian, such that both the overlaps between ground states of any two adjacent Hamiltonians, and the energy gap between the ground state and the first excited state of each Hamiltonian are not exponentially small. In comparison, for a specific type of problems where the usual quantum adiabatic algorithm fails, our algorithm remains to be efficient.Comment: 40 pages, 6 figures, more materials are adde