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 search for 95 GHz class I methanol masers in molecular outflows

We have observed a sample of 288 molecular outflow sources including 123 high-mass and 165 low-mass sources to search for class I methanol masers at 95 GHz transition and to investigate relationship between outflow characteristics and class I methanol maser emission with the PMO-13.7m radio telescope. Our survey detected 62 sources with 95 GHz methanol masers above 3$\sigma$ detection limit, which include 47 high-mass sources and 15 low-mass sources. Therefore the detection rate is 38% for high-mass outflow sources and 9% for low-mass outflow sources, suggesting that class I methanol maser is relatively easily excited in high-mass sources. There are 37 newly detected 95 GHz methanol masers (including 27 high-mass and 10 low-mass sources), 19 of which are newly identified (i.e. first identification) class I methanol masers (including 13 high-mass and 6 low-mass sources). Statistical analysis for the distributions of maser detections with the outflow parameters reveals that the maser detection efficiency increases with outflow properties (e.g. mass, momentum, kinetic energy and mechanical luminosity of outflows etc.). Systematic investigations of relationships between the intrinsic luminosity of methanol maser and the outflow properties (including mass, momentum, kinetic energy, bolometric luminosity and mass loss rate of central stellar sources) indicate a positive correlations. This further supports that class I methanol masers are collisionally pumped and associated with shocks, where outflows interact with the surrounding ambient medium.Comment: 32 pages, 5 figures, accepted by Ap

Synthesis and inclusion behavior of a heterotritopic receptor based on hexahomotrioxacalix[3]arene

A heterotritopic hexahomotrioxacalix[3]arene receptor with the capability of binding two alkali metals and a transition metal in a cooperative fashion was synthesized. The binding model was investigated by using ¹H NMR titration experiments in CDCl₃–CD₃CN (10:1, v/v), and the results revealed that the transition metal was bound at the upper rim and the alkali metals at the lower and upper rims. Interestingly, the alkali metal ions Li⁺ and Na⁺ bind at the lower and upper rim respectively depending on the dimensions of the alkali metal ions versus the size of the cavities formed by the calix[3]arene derivative. The hexahomotrioxacalix[3]arene receptor acts as a heterotritopic receptor, binding with the transition metal ion Ag⁺ and the alkali metals ions Li⁺ and Na⁺. These findings were not applicable to other different sized alkali metals, such as K⁺ and Cs⁺

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

Dimensionless ratios: characteristics of quantum liquids and their phase transitions

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multi-component quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel --- a novel and useful characteristic of multi-component Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realised multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin-degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.Comment: 12 pages (main paper), (6 figures