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

Septic Cavernous Sinus Thrombosis: An Unusual and Fatal Disease

BackgroundSeptic cavernous sinus thrombosis (CST) is a rare and fatal disease. Clinical presentations in the early stage are nonspecific, and the sensitivity of cranial axial computed tomography (CT) with thick section is low. This study analyzed the clinical manifestation and neuroimaging findings in patients with septic CST in a medical center in Taiwan.MethodsThis retrospective case series included nine patients with septic CST who had typical symptoms and clinical course, evidence of infection, and imaging studies which demonstrated cavernous sinus lesion, and who were treated between 1995 and 2003 at National Taiwan University Hospital.ResultsSeven (77.8 %) patients were more than 50 years old. Five (55.6%) had diabetes, and three (33.3%) had hematologic diseases. All cases were associated with paranasal sinusitis. The most frequent initial symptom was headache (66.7%), followed by ophthalmic complaints (diplopia or ophthalmoplegia, 55.6%; blurred vision or blindness, 55.6%), and ptosis (44.4%). Initial cranial images failed to identify CTS in all patients. Subsequent magnetic resonance imaging (MRI) or coronal contrast-enhanced CT (CECT) with thin section confirmed the diagnosis. Fungi were the most common pathogens (55.6%). The inhospital case-fatality rate was high (44.4%).ConclusionDue to the high case-fatality rate and low yield rate of blood cultures, fungal CST should be suspected in an immunocompromised patient with ophthalmic complaints that progress from one eye to the other. Coronal thin-section CECT may be a useful alternative to MRI as a diagnostic modality for this condition

Superconductivity and vortex structure on Bi2_{2}Te3_{3}/FeTe0.55_{0.55}Se0.45_{0.45} heterostructures with different thickness of Bi2_{2}Te3_{3} films

Using scanning tunnel microscopy (STM), we investigate the superconductivity and vortex properties in topological insulator Bi$_{2}$Te$_{3}$ thin films grown on the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$. The proximity-induced superconductivity weakens in the Bi$_{2}$Te$_{3}$ film when the thickness of the film increases. Unlike the elongated shape of vortex cores observed in the Bi$_{2}$Te$_{3}$ film with 2-quintuple-layer (QL) thickness, the isolated vortex cores exhibit a star shape with six rays in the 1-QL film, and the rays are along the crystalline axes of the film. This is consistent with the sixfold rotational symmetry of the film lattice, and the proximity-induced superconductivity is still topologically trivial in the 1-QL film. At a high magnetic field, when the direction between the two nearest neighbored vortices deviates from that of any crystalline axes, two cores connect each other by a pair of adjacent rays, forming a new type of electronic structure of vortex cores. On the 3-QL film, the vortex cores elongate along one of the crystalline axes of the Bi$_{2}$Te$_{3}$ film, similar to the results obtained on 2-QL films. The elongated vortex cores indicate a twofold symmetry of the superconducting gap induced by topological superconductivity with odd parity. This observation confirms possible topological superconductivity in heterostructures with a thickness of more than 2 QLs. Our results provide rich information for the vortex cores and vortex-bound states on the heterostructures consisting of the topological insulator and the iron-based superconductor.Comment: 8 pages, 8 figure