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Bulletin of the American Physical Society

Density Matrix Renormalization Group Study of a One Dimensional Three-Orbital Hubbard Model: The role of pair hopping and spin-flip interactions.

Nitin Kaushal, Guangkun Liu, Chris Bishop, Shuhua Liang, Shaozhi Li, Steven Johnston, Elbio R. Dagotto

Published Mar 16, 2016• 0 citations
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Charge-spin-orbital dynamics of one-dimensional two-orbital Hubbard model

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We study the real-time evolution of a charge-excited state in a one-dimensional $e_{\rm g}$-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the $z$ direction, electrons hop between adjacent $3z^2-r^2$ orbitals, while $x^2-y^2$ orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies $3z^2-r^2$ orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between $3z^2-r^2$ orbital and $x^2-y^2$ orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.

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We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor $t$ and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where $t$ $(>0)$ is much smaller than ${t}^{\ensuremath{'}}$ $(>0)$. First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral $t$ $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.

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Spin-triplet f-wave pairing due to three-site cyclic-exchange ferromagnetic interactions

Satoshi Nishimoto, Y. Ohta

Ferromagnetiam and superconductivity in a two-dimensional triangular-lattice Hubbard model are studied using the density-matrix renormalization group method. We propose a mechanism of the {\it f}-wave spin-triplet pairing derived from the three-site cyclic-exchange ferromagnetic interactions. We point out that a triangular network of hopping integrals, which is required for the three-site cyclic hopping processes, is contained in the (possibly) spin-triplet superconducting systems, such as Bechgaard salts (TMTSF)$_2$X, cobalt oxide Na$_{0.35}$CoO$_2$$\cdot$1.3H$_2$O, and layered perovskite Sr$_2$RuO$_4$.

arXiv:0810.3387•Oct 19, 2008•0 citations
We study the real-time evolution of a charge-excited state in a one-dimensional ege_{\rm g}eg​-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the zzz direction, electrons hop between adjacent 3z2−r23z^2-r^23z2−r2 orbitals, while x2−y2x^2-y^2x2−y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2−r23z^2-r^23z2−r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2−r23z^2-r^23z2−r2 orbital and x2−y2x^2-y^2x2−y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor ttt and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where ttt (>0)(>0)(>0) is much smaller than ${t}^{\ensuremath{'}}$ (>0)(>0)(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral ttt $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.
Ferromagnetiam and superconductivity in a two-dimensional triangular-lattice Hubbard model are studied using the density-matrix renormalization group method. We propose a mechanism of the {\it f}-wave spin-triplet pairing derived from the three-site cyclic-exchange ferromagnetic interactions. We point out that a triangular network of hopping integrals, which is required for the three-site cyclic hopping processes, is contained in the (possibly) spin-triplet superconducting systems, such as Bechgaard salts (TMTSF)2_22​X, cobalt oxide Na0.35_{0.35}0.35​CoO2_22​$\cdot1.3H1.3H1.3H_2O,andlayeredperovskiteSrO, and layered perovskite SrO,andlayeredperovskiteSr_2RuORuORuO_4$.