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Jisuan wuli

Spin-orbital Energy Gap in One-dimensional Spin-orbital Model

Rui Zhu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J_1/J_2=1/3.

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The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J_1/J_2=1/3.
We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling (J)(J)(J) at quarter filling, by using a density-matrix renormalization group method. At J=0J=0J=0, spin and orbital correlations coincide with each other with a peak at $q=\ensuremath{\pi}∕2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing JJJ, the peak position of orbital correlation changes to $q=\ensuremath{\pi}$, while that of spin correlation remains at $q=\ensuremath{\pi}∕2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.
To describe the spin-orbital energy gap formation in the one-dimensional symmetrically coupled spin-orbital model, we propose a simple mean-field theory based on an SU(4) constraint fermion representation of spins and orbitals. A spin-orbital gapped phase is formed due to a marginally relevant spin-orbital valence bond pairing interaction. The energy gap of the spin and orbital excitations grows extremely slowly from the SU(4)-symmetric point up to a maximum value and then decreases rapidly. By calculating the spin, orbital, and spin-orbital tensor static susceptibilities at zero temperature, we find a crossover from coherent to incoherent magnetic excitations as the spin-orbital coupling decreases from large to small values.
The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization-group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of coherent spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become incoherent. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.
In order to clarify a key role of the orbital degree of freedom in the spin S=1S=1S=1 Haldane system, we investigate ground-state properties of the t2g{t}_{2g}t2g​-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multiorbital systems, in general, there occurs a transition from an antiferromagnetic to a ferromagnetic phase. We find that the antiferromagnetic phase is described as the Haldane system with spin gap, while in the ferromagnetic phase, there exists the gapless excitation with respect to the orbital degree of freedom. Possible relevance of the present results to actual systems is also discussed.
Excitonic phases described by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-orbital Hubbard model with the Hund's rule coupling J . Using the variational cluster approximation, we calculate the ground-state energy and order parameters, and show that the Hund's rule coupling always stabilizes the excitonic spin-density- wave state and destabilizes the excitonic charge-density-wave state. The pair coherence lengths calculated in the spin-singlet and spin-triplet states indicate that only the spin-triplet excitons are paired more tightly with increasing J . The single-particle spectrum and density of states are also calculated to clarify the characters of these excitonic density-wave states.
In order to discuss the spin-gap formation in a multiorbital system, we analyze an eg{e}_{g}eg​-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an effective Heisenberg spin model including the correct effect of the orbital arrangement influenced by the spin excitation.