arXiv:cond-mat/0309067 · Physical Review B

Mott-Hubbard metal-insulator transition at noninteger filling

Krzysztof Byczuk, Walter Hofstetter, D. Vollhardt

Published Jan 29, 2004• 47 citations

Abstract

Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or $1+x$ the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction ${U}_{c}$ at which the metal-insulator transition occurs.

DOI: 10.1103/physrevb.69.045112

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arXiv:cond-mat/0309067 · Physical Review B

Mott-Hubbard metal-insulator transition at noninteger filling

Krzysztof Byczuk, Walter Hofstetter, D. Vollhardt

Published Jan 29, 2004• 47 citations

arXiv HTML PDF

Abstract

Correlated electrons in a binary alloy

{A}_{x}{B}_{1\ensuremath{-}x}

are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies

{\ensuremath{\epsilon}}_{i}

have a bimodal probability distribution and an energy separation

\ensuremath{\Delta}.

We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength

\ensuremath{\Delta}

and interaction U at different fillings. For filling factors

\ensuremath{\nu}=x

1+x

the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the

\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}

limit and find good agreement between analytical and numerical results for the critical interaction

{U}_{c}

at which the metal-insulator transition occurs.

DOI: 10.1103/physrevb.69.045112

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arXiv:cond-mat/0312390Physical Review BSep 29, 200449 citations

Correlated electrons in a binary alloy

{A}_{x}{B}_{1\ensuremath{-}x}

are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies

{\ensuremath{\epsilon}}_{i}

have a bimodal probability distribution and an energy separation

\ensuremath{\Delta}.

We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength

\ensuremath{\Delta}

and interaction U at different fillings. For filling factors

\ensuremath{\nu}=x

1+x

\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}

limit and find good agreement between analytical and numerical results for the critical interaction

{U}_{c}

at which the metal-insulator transition occurs.

W=4t

at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling

U_{\rm c}/t=4.45 \pm 0.05

. At

U=4.5t

, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at

U_{\rm c}

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.