Mott transition in correlated electron systems with orbital degree of freedom

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.

arXiv:0707.4535Physical Review LettersDec 7, 200739 citations

Mott transition in correlated electron systems with orbital degree of freedom

Yoshiaki Ōno, R. Bulla, Michael Potthoff

Published Jan 1, 2003• 0 citations

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Mott transitions in correlated electron systems with orbital degrees of freedom

Yūichi Ono, Michael Potthoff, R. Bulla

Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction ${U}_{\mathrm{c}}$ 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 $M=2.$ Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard model are studied by means of a generalization of the linearized dynamical mean-field theory. The method allows for an efficient and reliable determination of the critical interaction ${U}_{\mathrm{c}}$ 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 $M=2.$

arXiv:cond-mat/0206508Physical review. B, Condensed matterJan 30, 200380 citations

Critical Behaviour near the Mott Metal–Insulator Transition in a Two-Band Hubbard Model

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The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$ 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.The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$ 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.

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Stability of a metallic state in the two-orbital Hubbard model

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Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.

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Assessing the orbital selective Mott transition with variational wave functions

Luca F. Tocchio, Federico Arrigoni, Sandro Sorella +1 more

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.

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Quantum Phase Transition in the Two-Band Hubbard Model

Theo A. Costi, A. Liebsch

arXiv:0707.4535Physical Review LettersDec 7, 200739 citations

{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.