The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali-like atoms. We compute its static properties in the SU( $2M$ ) symmetric limit for up to $M=8$ bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on these unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy $M$ with high accuracy.The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali-like atoms. We compute its static properties in the SU($2M$) symmetric limit for up to $M=8$ bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on these unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy $M$ with high accuracy.

arXiv:1212.4485Physical Review BFeb 13, 201321 citations

Fermionization and Hubbard models

P. Dargis, Z. Maassarani

arXiv:cond-mat/9806208Nuclear Physics BDec 1, 199810 citations

Theory of electrons with orbital degeneracy

You‐Quan Li, Ulrich Eckern

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying ${\mathrm{SU}}_{d}(4)$ symmetry of spin-orbital double. A hidden charge ${\mathrm{SU}}_{c}(4)$ symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a $\mathrm{SO}(6)$ Heisenberg magnet at half-filling and a $\mathrm{SU}(4)$ one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.The Hubbard model for electrons with orbital degeneracy is shown to have an underlying ${\mathrm{SU}}_{d}(4)$ symmetry of spin-orbital double. A hidden charge ${\mathrm{SU}}_{c}(4)$ symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a $\mathrm{SO}(6)$ Heisenberg magnet at half-filling and a $\mathrm{SU}(4)$ one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.

arXiv:cond-mat/9911192Physical review. B, Condensed matterDec 15, 20005 citations

Effects of degenerate orbitals on the Hubbard model

昌久古賀, Akihisa Koga

Jan 1, 20030 citations

Finite-temperature Mott transitions in the multiorbital Hubbard model

Kensuke Inaba, Akihisa Koga, Sei-ichiro Suga +1 more

We investigate the Mott transitions in the multiorbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to fourfold degenerate bands. We discuss how the first-order Mott transition points ${U}_{c1}$ and ${U}_{c2}$ as well as the critical temperature ${T}_{c}$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.We investigate the Mott transitions in the multiorbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to fourfold degenerate bands. We discuss how the first-order Mott transition points ${U}_{c1}$ and ${U}_{c2}$ as well as the critical temperature ${T}_{c}$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.

arXiv:cond-mat/0506150Physical Review BAug 8, 200552 citations

On the one-dimensional Hubbard model away from half-filling

Andreas Schadschneider, J. Zittartz

The European Physical Journal BOct 1, 199110 citations

The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali-like atoms. We compute its static properties in the SU(

2M

) symmetric limit for up to

M=8

bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on these unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy

M

with high accuracy.

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying

{\mathrm{SU}}_{d}(4)

symmetry of spin-orbital double. A hidden charge

{\mathrm{SU}}_{c}(4)

symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a

\mathrm{SO}(6)

Heisenberg magnet at half-filling and a

\mathrm{SU}(4)

one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.

{U}_{c1}

and

{U}_{c2}

as well as the critical temperature

{T}_{c}

depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.