arXiv:cond-mat/9609176 · International Journal of Modern Physics B

Band Degeneracy and the Mott Transition: Dynamical Mean Field Study

Henrik Kajueter, Gabriel Kotliar

Published Mar 10, 1997• 33 citations

Abstract

We investigate the Mott transition in infinite dimensions in the orbitally degenerate Hubbard model. We find that the qualitative features of the Mott transition found in the one-band model are also present in the orbitally degenerate case. Surprisingly, the quantitative aspects of the density driven Mott transition around density one are not very sensitive to orbital degeneracy, justifying the quantitative success of the one-band model which was previously applied to orbitally degenerate systems. We contrast this with quantities that have a sizeable dependence on the orbital degeneracy and comment on the role of the intra-atomic exchange J.

DOI: 10.1142/s0217979297000411

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arXiv:cond-mat/9609176 · International Journal of Modern Physics B

Band Degeneracy and the Mott Transition: Dynamical Mean Field Study

Henrik Kajueter, Gabriel Kotliar

Published Mar 10, 1997• 33 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217979297000411

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{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.

{(U}_{c1})

and the one at which the metal becomes unstable

{(U}_{c2})

have a different dependence on the number of orbitals as the latter becomes large: ${U}_{c1}\ensuremath{\propto}\sqrt{N}$ while ${U}_{c2}\ensuremath{\propto}N.$ An exact analytical determination of the critical coupling

{U}_{c2}/N

is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.

{U}_{\mathrm{c}}

for any integer filling n and different M at zero temperature. For half filling a linear dependence of

{U}_{\mathrm{c}}

on M is found. Inclusion of the (full) Hund's rule exchange J results in a strong reduction of

{U}_{\mathrm{c}}.

The transition turns out to change qualitatively from continuous for

J=0

to discontinuous for any finite J. This result is confirmed using the exact-diagonalization method for

M=2.

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy

D

. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate (

D = 2

) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.