Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas

We discuss recent results on the relation between the strongly interacting one-dimensional Bose gas and a gas of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include the statistical profiles, the specific heat and local pair correlations. In the strong coupling limit $\gamma \to \infty$, the Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation from Fermi statistics during boson fermionization for finite but large interaction strength $\gamma$ is described by the relation $\alpha \approx 1 - 2/\gamma$, where $\alpha$ is a measure of the GES. This gives a quantitative description of the fermionization process. In this sense the recent experimental measurement of local pair correlations in a 1D Bose gas of $^{87}$Rb atoms also provides a measure of the deviation of the GES parameter $\alpha$ away from the pure Fermi statistics value $\alpha=1$. Other thermodynamic properties, such as the distribution profiles and the specific heat, are also sensitive to the statistics. They also thus provide a way of exploring fractional statistics in the strongly interacting 1D Bose gas.Comment: 7 pages, 4 figure

Ferromagnetic behaviour in the strongly interacting two-component Bose gas

We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat $c_v \sim T^{1/2}$ and the susceptibility $\chi \sim T^{-2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.Comment: 15 pages, 6 figures, revised version, references added, minor correction

Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases

We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H < H_{c1}$. A completely ferromagnetic phase without pairing occurs when the external field $H > H_{c2}$. In the region $H_{c1} < H < H_{c2}$ we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.Comment: 9 pages, 5 figures, expanded version with additional text, references and figure

Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases

We investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Analytic results in the limiting cases of strong and weak interactions are derived, where the Bosons are treated in the repulsive and the fermions in the strongly attractive regime. We confirm and complement results obtained previously from the Bethe ansatz equations in the thermodynamic limit.Comment: 12 pages, 1 figur

Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions

Using Yang and Yang's particle-hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general $SU(\kappa)$ fermionic system in one-dimension for both the repulsive and attractive regimes under the presence of an external magnetic field. These equations are derived from Sutherland's Bethe ansatz equations by using the spin-string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground state energies for both strongly repulsive and strongly attractive regimes.Comment: 22 pages, 2 figures, slight improvements, some extra reference

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

Allele imbalance in the transcriptome of human hepatocellular carcinoma: stress-induced gene plays a role

The two alleles of a gene are usually expressed equally in a normal cell, however, high incidence of allele-specific imbalance is frequently observed in cancer cells. Chromosomal regions with recurrent allele-specific imbalance usually harbor risk alleles and critical genes associated with cancer susceptibility and progression. With the development of large scale transcriptome sequencing technology, systematic analysis of the allele imbalance in the cancer transcriptome could be achieved at the single nucleotide resolution. In the April 2014 issue of Gastroenterology, we reported that the allele-specific imbalance of Oxidative Stress Induced Growth Inhibitor 1 (OSGIN1) can significantly contribute to the progression of HCC. OSGIN1 is a stress-induced pro-apoptotic protein. By validating the sequencing results in a cohort of HCC patients, we found the variant 438H form of OSGIN1 was specifically overrepresented in the tumor tissues. Functional studies indicated that OSGIN1 has strong tumor suppressive function in HCC both in vitro and in vivo. The pro-apoptotic function of the variant form of OSGIN1 was found to be less potent than the wild-type form, and the functional defects might be due to its poor efficiency to localize to the mitochondria. Clinical pathological analysis further revealed that the expression and genotype of OSGIN1 are closely associated with the prognosis of HCC patients. Taken together, our study linked the stress-induced genes with allele imbalance in HCC transcriptome, and proposed OSGIN1 to be an important tumor suppressor gene in the progression of HCC. Further characterization of OSGIN1 might help predict the prognosis of HCC patients and their responses to chemotherapeutic drugs.published_or_final_versio

Generalized exclusion statistics and degenerate signature of strongly interacting anyons

We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.Comment: 7 pages, 3 figures, expanded versio

Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure

The 1D interacting Bose gas in a hard wall box

We consider the integrable one-dimensional delta-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz. The ground state energy, including the surface energy, is derived from the Lieb-Liniger type integral equations. The leading and correction terms are obtained in the weak coupling and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann-Feynman theorem.Comment: 23 pages, 7 figures. Improved version. Extra figure added for the weak coupling regime. New expression for the interaction-dependent cloud size and additional reference