First R and I Lights and Their Photometric Analyses of GSC 02393-00680

We obtained complete $R$ and $I$ light curves of GSC 02393-00680 in 2008 and analyzed them with the 2003 version of the W-D code. It is shown that GSC 02393-00680 is a W-type shallow contact binary system with a high mass ratio $q=1.600$ and a degree of contact factor $f=5.0$. It will be a good example to check up on the TRO theory. A period investigation based on all available data suggests that the system has a small-amplitude period oscillation ($A_3=0.^{d}0030$; $T_3=1.92$years). This may indicate it has a moderate mass close third body, which is similar to XY Leo

Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type), which has a long correlation length $\xi\sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure

The tunnelling spectra of quasi-free-standing graphene monolayer

With considering the great success of scanning tunnelling microscopy (STM) studies of graphene in the past few years, it is quite surprising to notice that there is still a fundamental contradiction about the reported tunnelling spectra of quasi-free-standing graphene monolayer. Many groups observed V-shape spectra with linearly vanishing density-of-state (DOS) at the Dirac point, whereas, the others reported spectra with a gap of 60 meV pinned to the Fermi level in the quasi-free-standing graphene monolayer. Here we systematically studied the two contradicted tunnelling spectra of the quasi-free-standing graphene monolayer on several different substrates and provided a consistent interpretation about the result. The gap in the spectra arises from the out-of-plane phonons in graphene, which mix the Dirac electrons at the Brillouin zone corners with the nearly free-electron states at the zone center. Our experiment indicated that interactions with substrates could effectively suppress effects of the out-of-plane phonons in graphene and enable us to detect only the DOS of the Dirac electrons in the spectra. We also show that it is possible to switch on and off the out-of-plane phonons of graphene at the nanoscale, i.e., the tunnelling spectra show switching between the two distinct features, through voltage pulses applied to the STM tip.Comment: 4 Figure