arXiv:1008.3905 · Physical Review B

Two-site dynamical mean field theory for the dynamic Hubbard model

Giang H. Bach, J. E. Hirsch, F. Marsiglio

Published Oct 15, 2010• 13 citations

Abstract

At zero temperature, two-site dynamical mean field theory is applied to the dynamic Hubbard model. The dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasiparticle weight and the single-particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-type models.

DOI: 10.1103/physrevb.82.155122

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arXiv:1008.3905 · Physical Review B

Two-site dynamical mean field theory for the dynamic Hubbard model

Giang H. Bach, J. E. Hirsch, F. Marsiglio

Published Oct 15, 2010• 13 citations

arXiv HTML PDF

Abstract

U

in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasiparticle weight and the single-particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-type models.

DOI: 10.1103/physrevb.82.155122

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U

We study the Hubbard-Holstein model which includes both the electron-electron and electron-phonon interactions, characterized by

U

and

g

, respectively. The model is solved with

U

and

g

on an equal footing in the infinite dimensions by employing the dynamical mean-field theory in combination with Wilson's numerical renormalization group. A zero temperature phase diagram of symmetry unbroken states at half filling is mapped out which exhibits the interplay between the two kinds of interactions and combines the two separately studied interaction-driven metal-insulator transitions of the Hubbard and Holstein models within a single frame. The ground state is metallic when both

U

and

g

are small, but is insulating when

U

g

is large, referred to as, respectively, Mott-Hubbard insulator (MHI) and bipolaron insulator (BPI). As the phase boundary between the metallic and MHI (BPI) states is approached from the metallic region, the quasiparticle weight

z

goes to 0 continuously (discontinuously). Moreover, the two insulating states are distinct and cannot be adiabatically connected, and there is a first order phase transition between them.

U

, and the charge-transfer energy

Δ

between the

d

- and

p

-orbitals, transfer integrals

t_{pd}

t_{pp}

t_{dd}

between

p

d

p

p

and

d

d

sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.

{T}_{c}

superconductors). This leaves Fermi arcs that are closed into pockets by lines with very small quasiparticle residue.

1/3

filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.