Twisted Gauge Theory Model of Topological Phases in Three Dimensions

We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.Comment: 37 pages, 9 figures, 4 tables; revised to improve the clarity; references adde

Understanding and Predicting Delay in Reciprocal Relations

Reciprocity in directed networks points to user's willingness to return favors in building mutual interactions. High reciprocity has been widely observed in many directed social media networks such as following relations in Twitter and Tumblr. Therefore, reciprocal relations between users are often regarded as a basic mechanism to create stable social ties and play a crucial role in the formation and evolution of networks. Each reciprocity relation is formed by two parasocial links in a back-and-forth manner with a time delay. Hence, understanding the delay can help us gain better insights into the underlying mechanisms of network dynamics. Meanwhile, the accurate prediction of delay has practical implications in advancing a variety of real-world applications such as friend recommendation and marketing campaign. For example, by knowing when will users follow back, service providers can focus on the users with a potential long reciprocal delay for effective targeted marketing. This paper presents the initial investigation of the time delay in reciprocal relations. Our study is based on a large-scale directed network from Tumblr that consists of 62.8 million users and 3.1 billion user following relations with a timespan of multiple years (from 31 Oct 2007 to 24 Jul 2013). We reveal a number of interesting patterns about the delay that motivate the development of a principled learning model to predict the delay in reciprocal relations. Experimental results on the above mentioned dynamic networks corroborate the effectiveness of the proposed delay prediction model.Comment: 10 page

Distinct behaviors of suppression to superconductivity in LaRu3Si2LaRu_3Si_2 induced by Fe and Co dopants

In the superconductor LaRu$_3$Si$_2$ with the Kagome lattice of Ru, we have successfully doped the Ru with Fe and Co atoms. Contrasting behaviors of suppression to superconductivity is discovered between the Fe and the Co dopants: Fe-impurities can suppress the superconductivity completely at a doping level of only 3%, while the superconductivity is suppressed slowly with the Co dopants. A systematic magnetization measurements indicate that the doped Fe impurities lead to spin-polarized electrons yielding magnetic moments with the magnitude of 1.6 $\mu_B$\ per Fe, while the electrons given by the Co dopants have the same density of states for spin-up and spin-down leading to much weaker magnetic moments. It is the strong local magnetic moments given by the Fe-dopants that suppress the superconductivity. The band structure calculation further supports this conclusion.Comment: 6 pages, 7 figure