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arXiv:cond-mat/0310003 · Physical Review B

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

Hyun Cheol Lee, P. Azaria, E. Boulat

Published Apr 15, 2004• 27 citations
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Abstract

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.

DOI
10.1103/physrevb.69.155109

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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.
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.
We investigate dynamical symmetry enlargement in the half-filled SU(4) Hubbard chain using nonperturbative renormalization-group and quantum Monte Carlo techniques. A spectral gap is shown to open for arbitrary Coulombic repulsion UUU. At weak coupling, $U\ensuremath{\lesssim}3t$, a SO(8) symmetry between charge and spin-orbital excitations is found to be dynamically enlarged at low energy whereas at strong coupling, $U\ensuremath{\gtrsim}6t$, the charge degrees of freedom dynamically decouple. The crossover between these regimes is discussed.
We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U<0U<0U<0 using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of UUU, while the spin gap and others increase with increasing $\ensuremath{\mid}U\ensuremath{\mid}$ and have linear asymptotic behaviors.
We study a one-dimensional model of conduction electrons with a twofold-degenerate band away from half filling interacting via the Coulomb repulsion and Hund's rule coupling. We show that such a system has a divergent Cooper pair susceptibility at T=0T=0T=0, provided the Coulomb interaction UUU between electrons on the same orbital and the modulus of the Hund's exchange integral ∣J∣|J|∣J∣ are larger than the interorbital Coulomb interaction. The superconductivity can be achieved for any sign of JJJ. The opening of spectral gaps makes this state stable with respect to direct electron hopping between the orbitals. The scaling dimension of the superconducting order parameter lies between \textonequarter{} (small UUU) and \textonehalf{} (large UUU). Possible experimental realizations of such systems are discussed.
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.
The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings---strongest at half-filling---and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with nonlocal electron-phonon interactions, in addition to electron-electron interactions. This model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group (MFRG) for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of these dominant SC fluctuations and show that they arise because the spin-charge coupling at high energies is weakened by the nonlocal electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that nonlocal boson-mediated interactions may be important in the superconductivity observed in the organic superconductors.