Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $\Delta k_F$ ($2\Delta k_F$). Here $\Delta k_F=\pi(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch $k=\Delta k_F$, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter $\beta$ representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.Comment: 26 pages, 4 figures, published version, a series of study on the 1D attractive Hubbard model, few typos were corrected, references were added, also see arXiv:1708.07784 and arXiv:1708.0777

Phonon-lithium ion interactions: A case study of LiM(SeO3)2

Li ion diffusion is fundamentally a thermally activated ion hopping process. Recently, soft lattice, anharmonic phonon and paddlewheel mechanism have been proposed to potentially benefit the ion transport, while the understanding of vibrational couplings of mobile ion and anions is still limited but essential. Herein, we access the ionic conductivity, the stability and the lattice dynamics in LiM(SeO3)2 (M =Al, Ga, In, Sc, Y, and La) with two types of oxygen anions within LiO4 polyhedron, namely edge-shared and corner-shared, the prototype of which, LiGa(SeO3)2, has been experimentally synthesized. We studied in detail the anharmonic and harmonic phonon interactions, as well as couplings between vibrations of edge-bonded or corner-bonded anions in Li polyanions and Li ion diffusion. As M changing from Sc to La, anharmonic phonons increase alongside reduced activation energy for Li diffusion. Phonon modes involving edge-bonded oxygen anions contribute more to Li migration than corner-bonded oxygen anions, owing to greater atomic interactions between Li ions and edge-bonded anions. Thus, rather than the overall lattice softness, attentions shall be paid to reduce the frequency of the critical phonons contributing to Li ion diffusions as well as to increase the anharmonicity, for the design of Li ion superionic conductors for all-solid-state-batteries

DP-LTOD: Differential Privacy Latent Trajectory Community Discovering Services over Location-Based Social Networks

IEEE Community detection for Location-based Social Networks (LBSNs) has been received great attention mainly in the field of large-scale Wireless Communication Networks. In this paper, we present a Differential Privacy Latent Trajectory cOmmunity Discovering (DP-LTOD) scheme, which obfuscates original trajectory sequences into differential privacy-guaranteed trajectory sequences for trajectory privacy-preserving, and discovers latent trajectory communities through clustering the uploaded trajectory sequences. Different with traditional trajectory privacy-preserving methods, we first partition original trajectory sequence into different segments. Then, the suitable locations and segments are selected to constitute obfuscated trajectory sequence. Specifically, we formulate the trajectory obfuscation problem to select an optimal trajectory sequence which has the smallest difference with original trajectory sequence. In order to prevent privacy leakage, we add Laplace noise and exponential noise to the outputs during the stages of location obfuscation matrix generation and trajectory sequence function generation, respectively. Through formal privacy analysis,we prove that DP-LTOD scheme can guarantee \epsilon-differential private. Moreover, we develop a trajectory clustering algorithm to classify the trajectories into different kinds of clusters according to semantic distance and geographical distance. Extensive experiments on two real-world datasets illustrate that our DP-LTOD scheme can not only discover latent trajectory communities, but also protect user privacy from leaking