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arXiv:cond-mat/0308432 · Physical Review B

Phase diagram and symmetry breaking of an SU(4) spin-orbital chain in a generalized external field

Shi-Jian Gu, You‐Quan Li, Huan-Qiang Zhou

Published Apr 5, 2004• 4 citations
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Abstract

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.

DOI
10.1103/physrevb.69.144405

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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 one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4)\mathrm{SU}(4)SU(4) symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4)\mathrm{SU}(4)SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.
The one-dimensional S = 1 quantum spin chain with a linear and bilinear nearest-neighbour interaction of equal strength is integrable by the nested Bethe ansatz. In this paper the model is studied in the presence of an external magnetic field and an internal crystal field. By solving the Bethe ansatz equations for chains up to length N = 360 we construct the complete phase diagram of the system. We discuss how the magnetization curves depend on the internal field. In the SU(3) phase, where all three densities of atoms with -component -1, 0, +1 are non-vanishing, lines of constant density can be approximately parametrized by modified hypocycloides.
We study a one-dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with SU(4)\mathrm{SU}(4)SU(4) symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is SU(4)\mathrm{SU}(4)SU(4) invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.
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.
Using Yang and Yang's particle–hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general SU (κ) fermionic system in one dimension for both the repulsive and attractive regimes under the presence of an external magnetic field. These equations are derived from Sutherland's Bethe ansatz equations by using the spin–string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground-state energies for both strongly repulsive and attractive regimes.