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arXiv:cond-mat/0210436 · Physical review. B, Condensed matter

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

Shi-Jian Gu, You‐Quan Li

Published Sep 16, 2002• 12 citations
arXivHTMLPDF

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 ${g}_{t}=1.0$ differs from that for the case of ${g}_{t}=0.0.$ The magnetization curve and susceptibility are obtained for a system of 200 sites. For $0<{g}_{t}<{g}_{s},$ the phase diagram depending on the magnetic field and ratio of Land\'e factors, ${g}_{t}{/g}_{s},$ is obtained. Four phases with distinct magnetic properties are found.

DOI
10.1103/physrevb.66.092404

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Journal of Physics A Mathematical and General•Sep 21, 1992•6 citations
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{g}_{t}=1.0gt​=1.0 differs from that for the case of gt=0.0.{g}_{t}=0.0.gt​=0.0. The magnetization curve and susceptibility are obtained for a system of 200 sites. For 0<gt<gs,0<{g}_{t}<{g}_{s},0<gt​<gs​, the phase diagram depending on the magnetic field and ratio of Land'e factors, gt/gs,{g}_{t}{/g}_{s},gt​/gs​, is obtained. Four phases with distinct magnetic properties are found.
The ground-state phases of a one-dimensional SU(4) spin-orbital Hamiltonian in a generalized external field are studied on the basis of the Bethe-ansatz solution. Introducing three Land\'e g factors for spin, orbital, and their products in the SU(4) Zeeman term, we systematically discuss various symmetry breakings. The magnetization versus external field is evaluated by solving the Bethe-ansatz equations numerically. The phase diagrams corresponding to distinct residual symmetries are given by means of both numerical and analytical methods.
The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density-matrix renormalization-group technique. The method is applied to chains with up to 80 sites, and examined for test cases such as the one-dimensional spin-1/2 Heisenberg antiferromagnet whose excitation spectrum is known exactly from the Bethe ansatz. In the spin-orbital chain, the characteristic dynamical response depends strongly on the model parameters and the applied magnetic field. The coupling between the spin and orbital degrees of freedom is found to influence the incommensuration at finite magnetizations. In the regions of the phase diagram with only massive spin and orbital excitations, a finite field is required to overcome the spin gap. An orbital mode is found to become massless in this partially spin-polarized regime, indicating a strong coupling between the two degrees of freedom. In the critical region with three elementary gapless excitations, a prominent particle-hole excitation is observed at higher energies, promoted by the biquadratic term in the model Hamiltonian of the spin-orbital chain.
We study the effects of a uniform magnetic field on the one-dimensional spin-orbital model in terms of effective field theories. Two regions are examined: one around the SU(4) point (J=K/4)(J=K/4)(J=K/4) and the other with $K\ensuremath{\ll}J$ [see Eq. (1)]. We found that when J< K/4,J<~K/4,J< K/4, the spin and orbital correlation functions exhibit power-law decay with nonuniversal exponents. In the region with J>K/4,J>K/4,J>K/4, the excitation spectrum has a gap but the structure of it changes at different range of the ratio J/K.J/K.J/K. Furthermore, near the SU(4) point, the magnetic field exerts a great influence on the spectrum of the Sz=0{S}^{z}=0Sz=0 sector. When the magnetic field is beyond some critical value, a quantum phase transition occurs. The different structure of the excitation spectrum results in distinct critical behavior of correlation functions around the SU(4) point and the region with $K\ensuremath{\ll}J.$ Especially, the exponents in the latter case are universal.
We study the one-dimensional SU(4) exchange model under magnetic fields, which is the simplest effective Hamiltonian to investigate the orbital quantum fluctuations in coupled spin-orbit systems. The Bethe ansatz approaches and numerical calculations using the density matrix renormalization group method are employed. The main concern of the paper is how the system changes from the SU(4) to the SU(2) symmetric limit as the magnetic field is increased. For this model the conformal field theory predicts an unusual behavior: there is a jump of the critical exponents just before the SU(2) limit. For a finite-size system, however, the orbital-orbital correlation functions approach continuously the SU(2) limit after interesting crossover phenomena. The crossover takes place in the magnetization range 1/3--1/2 for the system with 72 sites studied in this paper.
By introducing a basis for a novel realization of the SU(4) Lie algebra, we exactly solve a spin-orbital chain with one-ion LLL-SSS coupling (OILSC) via the Bethe ansatz (BA) approach. In the context of different Landé ggg factors of the spin and orbital sectors, the OILSC results in rich and novel quantum phase transitions. Some accurate analytical expressions for the critical fields are obtained. Both spin ordering and orbital ordering are found in a gapped singlet phase. The system exhibits many interesting phenomena such as nonvanishing magnetization of the singlet phase, multi-entrance of the singlet in the ground state when the field varies, unsymmetric magnetization in two-component phase and magnetization crossover for different OILSC.
Starting with the known exact solution of the one-dimensional supersymmetric t-J model, the authors investigate ground-state properties of the system in the presence of an external magnetic field. By analytical calculations they find a representation of the magnetization curves and the susceptibility using the dressed charge matrix and the charge and spin densities: the dressed properties are given by a set of coupled integral equations which are derived from the Bethe ansatz equations in the thermodynamic limit. Some special results are found analytically, namely the magnetic field at which saturation occurs and the corresponding susceptibility. Furthermore they show the vanishing of the lower critical field. The dependence of magnetization and susceptibility on the magnetic field is calculated numerically for various particle densities.