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Chinese Physics Letters

One-Dimensional Two-Component Bosons with Attractive Interaction

Zhang Qiu-Lan

Published Dec 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/24/12/003

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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.
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.
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.
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 investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.