We consider the problem of consistence between the Bethe ansatz (BA) wave function and the multiparticle (more than two) scattering in one-dimensional δ-function interacting SU(4) fermions, which the approach of BA does not explicitly take into account. We find the scattering conditions of three and four particles located at the same position and show that the conditions can be fulfilled by the two-particle connection conditions of the BA wave function. So the definition of the BA wave function can be exactly extended to those cases with multiple occupancies. The inconsistence between the BA and multiparticle interacting on a same site in the degenerate Hubbard model, which makes the BA fail for the model, is shown to vanish in the limit of small site spacing. A correspondence relation of the BA equation and SU(4) symmetry of the system is also indicated for the fermions. The degeneracy of state with BA eigenenergy is given. Singlet lies in the case when there are equal numbers of particles in each inner component.
We consider the problem of consistence between the Bethe ansatz (BA) wave function and the multiparticle (more than two) scattering in one-dimensional δ-function interacting SU(4) fermions, which the approach of BA does not explicitly take into account. We find the scattering conditions of three and four particles located at the same position and show that the conditions can be fulfilled by the two-particle connection conditions of the BA wave function. So the definition of the BA wave function can be exactly extended to those cases with multiple occupancies. The inconsistence between the BA and multiparticle interacting on a same site in the degenerate Hubbard model, which makes the BA fail for the model, is shown to vanish in the limit of small site spacing. A correspondence relation of the BA equation and SU(4) symmetry of the system is also indicated for the fermions. The degeneracy of state with BA eigenenergy is given. Singlet lies in the case when there are equal numbers of particles in each inner component.
The same-position scattering (SPS) of more than two electrons in a one-dimensional model of two-band electrons with spin-exchange interaction is discussed. The boundary conditions of three- and four-particle SPS are given. It is shown that the conditions can be fulfilled by the two-particle boundary conditions for the Bethe ansatz (BA) wavefunction. Consequently, the definition of the BA wavefunction can be extended to those cases of more than two particles occupying the same position. Therefore, unlike the case in lattice models in which configurations with more than two particles at one site are excluded in applying the approach, the BA is valid without the exclusion of multi-particle SPS in the spin-exchange model. A relation between the SU (2) × SU (2) symmetry and the BA equation is also indicated.
A Hubbard-like model with SU(4) symmetry for electrons with twofold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite N number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving Bethe-ansatz equation numerically. For infinite N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit.
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.
Abstract. – We study a one-dimensional Bose system with repulsive δ-function interaction in the presence of an SU(2) intrinsic degree of freedom on the basis of the coordinate Betheansatz. The ground state and the low-lying excitations are determined by both numerical and analytical methods. It is shown that the ground state is an isospin-ferromagnetic state, and the excitations are composed of three elementary particles: holons, antiholons, and isospinons. The isospinon is a triplet coupled to the “ferromagnetic ” background anti-parallelly. Exactly solvable models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] play an important role in physics, specifically in the investigation of one-dimensional (1D) interacting many-particle systems. They have served as a source of inspiration for the understanding of non-perturbative phenomena in correlated electronic systems; e. g., the spinon was explicitly characterised on the basis of the exact solution of the Hubbard model [6]. Among these models, an earlier prototypical one is the model of 1D bosons with repulsive δ-function interaction, which was solved [7] by means of the Bethe-ansatz. This method was also applied to solve the problem of spin-1/2 fermions [8,9] with δ-function interaction; in fact, Yang [9] already suggested a general strategy for multi-component systems. Various extensions include the study of electrons on
The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.
In this paper, we solve one-dimensional SU (3) bosons with repulsive δ-function interaction using the Bethe ansatz method. The features of the ground and low-lying excited states are studied by both numerical and analytical methods. We show that the ground state is a SU (3) colour ferromagnetic state. The configurations of quantum numbers for the ground state are given explicitly. For a finite N system, the spectra of low-lying excitations and the dispersion relations of four possible elementary particles (holon, antiholon, σ-coloron and ω-coloron) are obtained by solving the Bethe ansatz equation numerically. The thermodynamic equilibrium of the system at finite temperature is studied by using the strategy of the thermodynamic Bethe ansatz; we give a revised Gaudin–Takahashi equation which is useful for the numerical method. Thermodynamic quantities, such as specific heat, are obtained for some special cases. We find that the magnetic property of the model in the high-temperature regime is dominated by Curie's law, χ ∝ 1/ T , and the system has Fermi-liquid-like specific heat in the strong coupling limit at low temperature.