Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions

Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory.Comment: 13 pages, 4 figure

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

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

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference

Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions

We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.Comment: 4 pages, 3 figures, minor revisions to text, replacement figure, refs added and update

Coulomb Driven New Bound States at the Integer Quantum Hall States in GaAs/Al(0.3)Ga(0.7)As Single Heterojunctions

Coulomb driven, magneto-optically induced electron and hole bound states from a series of heavily doped GaAs/Al(0.3)Ga(0.7)As single heterojunctions (SHJ) are revealed in high magnetic fields. At low magnetic fields (nu > 2), the photoluminescence spectra display Shubnikov de-Haas type oscillations associated with the empty second subband transition. In the regime of the Landau filling factor nu < 1 and 1 < nu <2, we found strong bound states due to Mott type localizations. Since a SHJ has an open valence band structure, these bound states are a unique property of the dynamic movement of the valence holes in strong magnetic fields