One dimensional SU(3) bosons with $\delta$ function interaction

TL;DR

This paper solves one-dimensional SU(3) bosons with delta interaction using Bethe ansatz, analyzing ground states, excitations, and thermodynamics, revealing ferromagnetic ground states and Fermi-liquid behavior at low temperatures.

Contribution

It provides an exact solution for the SU(3) boson model, including explicit quantum number configurations and thermodynamic properties, extending understanding of multi-component quantum gases.

Findings

Ground state is SU(3) color ferromagnetic.

Spectra of low-lying excitations are obtained numerically.

System exhibits Curie law and Fermi-liquid like specific heat.

Abstract

In this paper we solve one dimensional SU(3) bosons with repulsive $\delta$-function interaction by means of Bethe ansatz method. The features of ground state and low-lying excited states are studied by both numerical and analytic methods. We show that the ground state is a SU(3) color ferromagnetic state. The configurations of quantum numbers for the ground state are given explicitly. For finite $N$ system the spectra of low-lying excitations and the dispersion relations of four possible elementary particles (holon, antiholon, $\sigma$-coloron and $\omega$-coloron) are obtained by solving Bethe-ansatz equation numerically. The thermodynamic equilibrium of the system at finite temperature is studied by using the strategy of thermodynamic Bethe ansatz, a revised Gaudin-Takahashi equation which is useful for numerical method are given . The thermodynamic quantities, such as specific heat, are obtain for some special cases. We find that the magnetic property of the model in high temperature regime is dominated by Curie's law: $\chi\propto 1/T$ and the system has Fermi-liquid like specific heat in the strong coupling limit at low temperature.