The interaction between itinerant and Mott localized electronic states in strongly correlated materials is studied within dynamical mean field theory in combination with the numerical renormalization group method. A novel nonmagnetic zero temperature quantum phase transition is found in the bad-metallic orbital-selective Mott phase of the two-band Hubbard model, for values of the Hund's exchange which are relevant to typical transition metal oxides.

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Mott transition at large orbital degeneracy: Dynamical mean-field theory

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arXiv:cond-mat/0206508 · Physical review. B, Condensed matter

Mott transitions in correlated electron systems with orbital degrees of freedom

Yūichi Ono, Michael Potthoff, R. Bulla

Published Jan 30, 2003• 80 citations

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Abstract

{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.

DOI: 10.1103/physrevb.67.035119

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{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.

U

at the

d

-orbital and the charge-transfer energy

Δ

between the

d

- and

p

-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of

U

and

Δ

. The analytic results are in good agreement with the numerical results of the exact diagonalization method.

{(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.