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Chinese Journal of Physics

Excitations and Thermodynamics of One-Dimensional Boson System with δ-Function Interaction

Tien-Ke Lai, Cherng-Hsiao Lin, Chin-Rong Lee, Hsiang-nan Li

Published Oct 1, 1995• 1 citation
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Abstract

We present the excitation spectra of a one-dimensional boson system with b-function interaction, which includes a velocity-dependent pseudopotential. The equilibrium thermodynamics of the system is studied and the behavior of the particle distribution at different temperature is given. The effects from the velocity-dependent interaction are analyzed. We address also on the question whether a one-dimensional fermion system with this pseudopotential is solvable.

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We present the excitation spectra of a one-dimensional boson system with b-function interaction, which includes a velocity-dependent pseudopotential. The equilibrium thermodynamics of the system is studied and the behavior of the particle distribution at different temperature is given. The effects from the velocity-dependent interaction are analyzed. We address also on the question whether a one-dimensional fermion system with this pseudopotential is solvable.
The interplay of quantum statistics, interactions, and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential, and either the total chemical potential or a fixed number of particles, allowing quantification of the full crossover behavior of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction.
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.
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.