Magnetic properties of an SU(4) spin-orbital chain

Abstract

In this paper, we study the magnetic properties of the one-dimensional SU(4) spin-orbital model by solving its Bethe ansatz solution numerically. It is found that the magnetic properties of the system for the case of gt = 1.0 differs from that for the case of gt = 0.0. The magnetization curve and susceptibility are obtained for a system of 200 sites. For 0 < gt < gs, the phase diagram depending on the magnetic field and the ratio of Landé factors, gt/gs, is obtained. Four phases with distinct magnetic properties are found.PACS number:75.30. Kz,75.10.Jm, Recently, much attention has been focused on strongly correlated electrons with orbital degrees of freedom [1,2,3,4,5,6,7] due to progress in experimental studies of transition metal and rare earth compounds such as LaMnO 3 , CeB 6 and TmTe. Examples of spin-orbital systems in one dimension include quasi-one-dimensional tetrahis-dimethylamino-ethylene(TDAE)-C 60 [8], artificial quantum dot arrays [9] and degenerate chains in Na 2 Ti 2 Sb 2 O and Na 2 V 2 O 5 compounds [10,11,12]. In these systems, the low-lying electron states have orbital degeneracy in addition to the spin degeneracy. This may result in various interesting properties associated with the orbital degrees of freedom in Mott insulating phases. For example, the magnetic ordering is influenced by the orbital structure which may change with pressure, or the magnetization is a nonlinear function of magnetic field even in the case of an isotropic exchange interaction ofThe spin model with orbital degeneracy in a magnetic field was studied by means of effective field theories [5] recently. It has been shown that there exists critical behavior under magnetic field. For a nonperturbative understanding of the magnetic properties of the model, the Bethe-ansatz solution of the SU(4) model is applicable when the exterior magnetic field is applied since the total z component of spin and orbital is a good quantum number. Although Ref.[6] studied the magnetic properties in terms of the Bethe-ansatz method, their result involves only a special case because the Landé factor was not taken into account. In present paper, we study the model in the presence of an exterior field by solving the Bethe-ansatz equation numerically meanwhile taking account of the Landé g factor. We obtain a rich phase diagram in comparison to what was obtained in [6]. Our results shed new light on the understanding of more realistic systems. The quantum phase transition(QPT) [14] concluded from such a system is speculated to be found in experiments.The one-dimensional quantum spin 1/2 system with twofold orbital degeneracy is modelled by [15,16] where the coupling constant is set to unity. The Hamiltonian (1) has not only SU(2)×SU(2) symmetry, but also an enlarged SU(4) symmetry [16]. It was solved by the Bethe-ansatz approach, the obtained secular equation reads [17,18]:where θ ρ (x) = −2 tan −1 (x/ρ). The quantum numbers {I a , J a , K a } specify a state in which there are N − M number of sites in the state • {I a , J a , K a } are consecu...

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