Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.     

Properties of One-Dimensional Highly Polarized Fermi Gases

Using both the exact Bethe ansatz method and the variational method, we study properties of the one-dimensional Fermi polaron. We focus on the binding energy, effective mass, momentum distributions, Tan contact and correlation functions. As the attraction increases, the impurity is more tightly bound and correlated with the surrounding particles, and the size of formed polaron decreases. In addition, compared with the Bethe ansatz method, the variational method is totally qualified to study the one-dimensional Fermi polaron. The intrinsic reason is that the number of particle-hole excitations in a Fermi sea, caused by a single impurity, is always rather small. The variational method can be well extended to other impurity systems.     

Collective modes of type-ⅡWeyl fermions with repulsive S-wave interaction

Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.     

Toda solitons as Fermi-quasiparticles

The Bethe ansatz leads to Yang-Yang integral equations. The particle-hole structure of the zero-temperature excitations is generalized to finite temperatures, which leads to the definition of soliton- and phonon-quasiparticles. The solitons approximately follow the Fermi-Dirac statistics and have a chemical potential with an unusual temperature dependence, because the number of solitons is not constant.     

Exact solution of the general non-intersecting string model

We present a thorough analysis of the non-intersecting string (NIS) model and its exact solution. This is an integrable q-states vertex model describing configurations of non-intersecting polygons on the lattice. The exact eigenvalues of the transfer matrix are found by the analytic Bethe ansatz. The Bethe ansatz equations thus found are shown to be equivalent to those for a mixed spin model involving both and infinite spin. This indicates that the NIS model provides a representation of the quantum group corresponding to spins and s = ∞. The partition function and the excitations in the thermodynamic limit are computed.     

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 ground-state 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.     

Critical exponents of a multicomponent anisotropict−J model in one dimension

A recently presented anisotropic generalization of the multicomponent supersymmetrict–J model in one dimension is investigated. This model of fermions with general spin-S is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses 2S massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of 2S+1 fermions with finite binding energy. The critical behaviour is described by ac=1 conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Giant charge relaxation resistance in the Anderson model

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance peak fades away at the particle-hole symmetric point.     

Composite-fermion spin excitations as nu approaches 1/2: interactions in the Fermi sea

Measurements of low-lying spin excitations by inelastic light scattering unveil a delicate balance between spin reversal and Fermi energies in the Fermi sea of composite fermions that emerges in the limit of nu --> 1/2. The interplays between these two fundamental quasiparticle interactions are uncovered in lowest spin-flip excitations in which the spin orientation and Landau level index of composite fermions change simultaneously. A collapse of the spin-flip excitation gap as nu --> 1/2 is linked to vanishing quasiparticle energy level spacings and loss of full spin polarization.     

Non-equivalence between Heisenberg XXZ spin chain and Thirring model

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the antiferromagnetic case. We examine the relation between the XXZ spin chain and the massless Thirring model, and show that the spectrum of the XXZ spin chain has a gapless excitation while the regularized Thirring model calculated with the Bogoliubov transformation method has a finite gap. This finite gap spectrum is also confirmed by the Bethe ansatz solution of the massless Thirring model.Received: 28 October 2004, Published online: 21 January 2005PACS: 10.Kk, 03.70. + k, 11.30.-j, 11.30.Rd     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb–Wu equations

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model. Specifying the parameters appropriately, we obtain the Bethe ansatz equations of the supersymmetric t-J model, the Hubbard model, or of Yang's model of electrons with delta interaction. This means that the Bethe ansatz equations of these (and many other) models can be obtained from a common algebraic source, namely from the Yang–Baxter algebra generated by the gl(1|2) invariant R-matrix.     

Ground and excited states of spinor fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model

The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.     

Spin drag and spin-charge separation in cold fermi gases

Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes, however, can decay due to several possible mechanisms. In this Letter we expose a new facet of spin-charge separation: not only the speeds but also the damping rates of spin and charge excitations are different. While the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive. We suggest that cold Fermi gases trapped inside a tight atomic waveguide offer the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet.     

Exact solution of an anisotropic J_1–J_2 model with the Dzyloshinsky–Moriya interactions at boundaries

We propose a method to construct new quantum integrable models. As an example, we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor, next-nearestneighbor and chiral three-spin couplings. It is shown that the boundary fields can enhance the anisotropy of the first and last bonds, and can induce the Dzyloshinsky–Moriya interactions along the z-direction at the boundaries. By using the algebraic Bethe ansatz, we obtain the exact solution of the system. The energy spectrum of the system and the associated Bethe ansatz equations are given explicitly. The method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.     

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous X X X Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.     

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.