Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction

Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $\mu$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2$ and correlation length exponent $\nu=1/2$ read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with $SU(N)$ symmetry.Comment: 20 pages, 5 figures, submitted to J.Phys.A, revised versio

Exotic pairing in 1D spin-3/2 atomic gases with SO(4)SO(4) symmetry

Tuning interactions in the spin singlet and quintet channels of two colliding atoms could change the symmetry of the one-dimensional spin-3/2 fermionic systems of ultracold atoms while preserving the integrability. Here we find a novel $SO(4)$ symmetry integrable point in thespin-3/2 Fermi gas and derive the exact solution of the model using the Bethe ansatz. In contrast to the model with $SU(4)$ and $SO(5)$ symmetries, the present model with $SO(4)$ symmetry preserves spin singlet and quintet Cooper pairs in two sets of $SU(2)\otimes SU(2)$ spin subspaces. We obtain full phase diagrams, including the Fulde-Ferrel-Larkin-Ovchinnikov like pair correlations, spin excitations and quantum criticality through the generalized Yang-Yang thermodynamic equations. In particular, various correlation functions are calculated by using finite-size corrections in the frame work of conformal field theory. Moreover, within the local density approximation, we further find that spin singlet and quintet pairs form subtle multiple shell structures in density profiles of the trapped gas.Comment: 8 figures, 2 tables, 37 page

Many-body properties of quasi-one dimensional Boson gas across a narrow CIR

We study strong interaction effects in a one-dimensional (1D) Boson gas across a narrow confinement induced resonance (CIR). In contrast to the zero range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative $\delta$-function interaction on many-body level. Using the asymptotic Bethe ansatz, we find that the low energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by an effective finite range parameter $v$. This parameter drastically alters quantum criticality and universal thermodynamics of the gas. In particular, it drives the Tonks-Girardeau (TG) gas from non-mutual Fermi statistics to mutual statistics or to a more exclusive super TG gas. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.Comment: 5.2 pages, 4 figures, final version accepted by EP

Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions

The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the Néel antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional p-wave interactions. In this strong-coupling limit, the 1D trapped Fermi gas exhibits an effective Heisenberg spin XXZ chain in the anisotropic p-wave scattering channels. For a particular p-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the antiferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of K40 atoms with very close s-wave and p-wave Feshbach resonances.This work is supported by the National Natural Science Foundation of China (NNSFC) under Grants No. 11374177, No. 11421092, and No. 11374331, and by key NNSFC Grant No. 11534014, by the National Basic Research Program of China under Grant No. 2012CB922101, and the programs of the Chinese Academy of Sciences. X.W.G. and X.C. thank Y-Z. Jiang, D. Kurlov, G. Shlyapnikov, and Y.-P. Wang for helpful discussions

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions

The low temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener-Hopf method. It is shown that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(3) Heisenberg spin chain. Beyond the Tomonaga-Luttinger liquid regime, the equation of state is given in terms of the polylog function for a weak external field. The results obtained are essential for further study of quantum criticality in strongly repulsive three-component fermions.Comment: 21 pages, 2 figure