Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter filling. This model is equivalent to the Bethe soluble SU(4) exchange model. Quantum numbers of the ground state and the lowest branch of excitations are determined. The spin-spin correlation functions are obtained numerically by the density matrix renormalization group method. It shows a power-law decay with oscillations of the period of four sites. The period originates from the interference between the spin and orbital degrees of freedom. The exponent of the power-law decay estimated from the finite size data is consistent with the prediction by the conformal field theory.
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) and the other with $K\ensuremath{\ll}J$ [see Eq. (1)]. We found that when
J< K/4, the spin and orbital correlation functions exhibit power-law decay with nonuniversal exponents. In the region with
J>K/4, the excitation spectrum has a gap but the structure of it changes at different range of the ratio
J/K. Furthermore, near the SU(4) point, the magnetic field exerts a great influence on the spectrum of the
Sz=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 effect of symmetry-breaking perturbations in the one-dimensional
SU(4) spin-orbital model. We allow the exchange in spin
(J1) and orbital
(J2) channel to be different and thus reduce the symmetry to $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{SU}(2).$ A magnetic field
h along the
Sz direction is also applied. Using the formalism developed by Azaria et al. [Phys. Rev. Lett.
83, 624 (1999)] we extend their analysis of the isotropic
J1=J2, h=0 case and obtain the low-energy effective theory near the
SU(4) point in the generic case ${J}_{1}\ensuremath{\ne}{J}_{2},$ $h\ensuremath{\ne}0.$ In zero magnetic field, we retrieve the same qualitative low-energy physics as in the isotropic case. In particular, the isotropic massless behavior found on the line
J1=J2<K/4 extends in a large anisotropic region. We discover, however, that the anisotropy plays its trick in allowing nontrivial scaling behaviors of the physical quantities. For example, the mass gap
M has two different scaling behaviors depending on the anisotropy. In addition, we show that in some regions, the anisotropy is responsible for anomalous finite-size effects and may change qualitatively the shape of the computed critical line in a finite system. When a magnetic field is present the effect of the anisotropy is striking. In addition to the usual commensurate-incommensurate phase transition that occurs in the spin sector of the theory, we find that the field may induce a second transition of the KT type in the remaining degrees of freedom to which it does not couple directly. In this sector, we find that the effective theory is that of an SO(4) Gross-Neveu model with an $h\ensuremath{-}\mathrm{dependent}$ coupling that may change its sign as
h varies.
By introducing a basis for a novel realization of the SU(4) Lie algebra, we exactly solve a spin-orbital chain with one-ion
L-
S coupling (OILSC) via the Bethe ansatz (BA) approach. In the context of different Landé
g 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.
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 ratio of Land\'e factors,
gt/gs, is obtained. Four phases with distinct magnetic properties are found.
We numerically study the SU(2)
⊗SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum
q=π form massless continua which split from the excitations belonging to the
[22] irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around
q=π/2 originating from [
2112] become critical, too.