FFLO correlation and free fluids in the one-dimensional attractive Hubbard model

In this Rapid Communication we show that low energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially-polarized phase. We then show that for such a FFLO-like state in the low density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility and specific heat obey simple additivity rules, indicating the `free' particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility which provide universal macroscopic properties/dimensionless constants of interacting fermions at low energy.Comment: In this Letter we analytically study FFLO pairing correlation and the universal nature of the FFLO-like state. More detailed studies of this model will be presented in arXiv:1710.08742 and arXiv:1708.0778

A words-of-interest model of sketch representation for image retrieval

In this paper we propose a method for sketch-based image retrieval. Sketch is a magical medium which is capable of conveying semantic messages for user. It’s in accordance with user’s cognitive psychology to retrieve images with sketch. In order to narrow down the semantic gap between the user and the images in database, we preprocess all the images into sketches by the coherent line drawing algorithm. During the process of sketches extraction, saliency maps are used to filter out the redundant background information, while preserve the important semantic information. We use a variant of Words-of-Interest model to retrieve relevant images for the user according to the query. Words-of-Interest (WoI) model is based on Bag-ofvisual Words (BoW) model, which has been proven successfully for information retrieval. Bag-of-Words ignores the spatial relationships among visual words, which are important for sketch representation. Our method takes advantage of the spatial information of the query to select words of interest. Experimental results demonstrate that our sketch-based retrieval method achieves a good tradeoff between retrieval accuracy and semantic representation of users’ query

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

Exact results of dynamical structure factor of Lieb-Liniger model

The dynamical structure factor (DSF) represents a measure of dynamical density-density correlations in a quantum many-body system. Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large Hilbert space, such kind of dynamical correlations often impose a big theoretical challenge. For one dimensional (1D) quantum many-body systems, qualitative predictions of dynamical response functions are usually carried out by using the Tomonaga-Luttinger liquid (TLL) theory. In this scenario, a precise evaluation of the DSF for a 1D quantum system with arbitrary interaction strength remains a formidable task. In this paper, we use the form factor approach based on algebraic Bethe ansatz theory to calculate precisely the DSF of Lieb-Liniger model with an arbitrary interaction strength at a large scale of particle number. We find that the DSF for a system as large as 2000 particles enables us to depict precisely its line-shape from which the power-law singularity with corresponding exponents in the vicinities of spectral thresholds naturally emerge. It should be noted that, the advantage of our algorithm promises an access to the threshold behavior of dynamical correlation functions, further confirming the validity of nonlinear TLL theory besides Kitanine et. al. 2012 J. Stat. Mech. P09001. Finally we discuss a comparison of results with the results from the ABACUS method by J.-S. Caux 2009 J. Math. Phys. 50 095214 as well as from the strongly coupling expansion by Brand and Cherny 2005 Phys. Rev. A 72 033619.Comment: 20 pages, 5 figure

Exact Spectral Function of One-Dimensional Bose Gases

Strong correlation in one-dimensional (1D) quantum systems drastically changes their dynamic and transport properties in the presence of the interaction. In this letter, combining quantum integrable theory with numerics, we exactly compute the spectral function of 1D Lieb-Liniger gas at a many-body level of large scales. It turns out that a full capture of the power-law singularities in the vicinities of thresholds requires system size as large as thousands of particles. Our research essentially confirms the validity of the nonlinear Tomonaga-Luttinger liquid and provides a reliable technique for studying critical behaviour emerged only in thermodynamic limit.Comment: 6 pages, 3 figures, Supplementary Materia

Shadow of general rotating black hole

The Johannsen black hole (BH) is a generic rotating BH admitting three constants of motions ( energy, angular momentum and Carter constant) and is characterized by four deviation parameters besides mass and spin, which could be a model-independent probe of the no-hair theorem. We study the effects of the deviation parameters on the BH shadow as well as the effects of spin. By using the shadow boundaries of M87* and SgrA*, for the fist time, the deviation parameters of are constrained. The detail results depend on the spin $a$ and inclination angle $\theta_0$. Assuming $a=0.2$ and $\theta_0=15^{\circ}$, the deviation parameter $\alpha_{13}$ are constained within $\sim$ [-3.5, 6] for M87* observation and [-3, 0.5] for SgrA* observation. We also show the images of a Johannsen BH surrounded by a Page-Thorne thin accretion disk observed by a remote observer with a ray-tracing method, and discuss the effects of the deviation parameters on deforming the accretion disk image, which could be tested by observations with higher sensitivities in the future.Comment: 14 pages, 9 figure

Poly[[aqua­(1-naphthyl­acetato)cadmium(II)]-μ3-pyridin-3-olato]

In the title complex, [Cd(C5H4NO)(C12H9O2)(H2O)]n, each CdII atom is coordinated by two carboxylate O atoms from one 1-naphthyl­acetate ligand, two hydroxyl O atoms from two pyridin-3-olate ligands, one N atom from another pyridin-3-olate ligand and one water mol­ecule, and displays a distorted octa­hedral coordination geometry. The compound forms infinite chains of pyridin-3-olate ligands bridging 1-naphthyl­acetate–CdII units parallel to the b axis, with a Cd⋯Cd separation of 3.578 (2) Å. The chains are further self-assembled into a supra­molecular network through inter­molecular O—H⋯O hydrogen-bonding inter­actions

Tricyclo­hex­yl(3,5-dibromo-2-hy­droxy­benzoato-κO)tin(IV)

In the title compound, [Sn(C6H11)3(C7H3Br2O3)], the Sn atom is four-coordinate and possesses a distorted Sn(C3O) tetra­hedral geometry, with Sn—C bond lengths in the range 2.132 (6)–2.144 (6) Å and with Sn—O = 2.086 (4) Å. The uncoordinated carboxyl­ate O atom forms a weak contact with the Sn atom, with an Sn⋯O separation of 2.962 (2) Å