Ground state and low-lying excitations in the one-dimensional anisotropic SU(2) thirring model

Jize Zhao, Kazuo Ueda, Xiaoqun Wang

Ryuhei Sato

The one-dimensional anisotropic t - J model was exactly solved using the Bethe ansatz . We first discuss the effect of anisotropy on the ground-state properties. We find a continuous phase transition induced by a magnetic field. The low-lying (spin and charge) excitation spectrum is obtained for various fillings. According to the anisotropy, the model has massive or massless modes for spin excitations. At half-filling, the model reduces to the spin- antiferromagnetic XXZ -model. We calculate the correct excitation continuum whose lowest mode is lower than that obtained by des Cloizeaux and Gaudin. Charge excitations are massless for any value of the anisotropy.

Jenő Sólyom, Timothy A. L. Ziman

The ground state and low-lying excited states of a one-dimensional Heisenberg model with axial anisotropy are studied by extrapolation from finite lattices. The ground-state properties and the phase diagram are determined for quantum spins, especially for $S=\frac{1}{2}, 1, \mathrm{and} \frac{3}{2}$. Higher spin values do not give new features in the phase diagram. the limitations of finite-lattice extrapolation are discussed in connection with the possibility of a singlet phase for the $S=1$ isotropic Heisenberg antiferromagnet.

Lyudvig Dmitrievich Faddeev, Leon Armenovich Takhtadzhyan

G. Uimin, С. В. Фомичев

You-quan Li, Shi-jian Gu, Zu-jian Ying +1 more

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