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Exact results of the ground state and excitation properties of a two-component interacting Bose system

You-quan Li, Shi-jian Gu, Zu-jian Ying, Ulrich Eckern

Published Jan 1, 2002• 21 citations
OpenAlex

Abstract

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

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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
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 Bethe ansatz. 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.
In this paper we solve one-dimensional trapped SU (2) bosons with repulsive δ-function interaction by means of the Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin `ferromagnetic' state which differs from spin-½ fermion systems. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The equilibrium thermodynamics of the system at finite temperature is studied using the thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat, etc, are obtained for the case of the strong coupling 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.
On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and δ-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like T at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.
The Bethe-ansatz method is used to solve one-dimensional two-component bosons with a δ-function potential considering the negative coupling constant part. With the string hypothesis of Minoru Takahashi, the features of the ground state and low-lying excited states of this model are discussed explicitly by analytical and numerical methods. Especially for a N = 2 system, the two bosons being pairs is obvious, and the ground state which is independent of the coupling constant should be ferromagnetic.
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.