arXiv:cond-mat/0012329 · Physical review. B, Condensed matter

Finite-temperature numerical renormalization group study of the Mott transition

R. Bulla, Theo A. Costi, D. Vollhardt

Published Jun 28, 2001• 281 citations

Abstract

Wilson's numerical renormalization group method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean-field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real-frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for $T<{T}_{\mathrm{c}}\ensuremath{\approx}0.02W$ $(W:$ bandwidth) we find hysteresis with first-order transitions both at ${U}_{\mathrm{c}1}$ (defining the insulator to metal transition) and at ${U}_{\mathrm{c}2}$ (defining the metal to insulator transition), at $T>{T}_{\mathrm{c}}$ there is a smooth crossover from metalliclike to insulatinglike solutions.

DOI: 10.1103/physrevb.64.045103

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arXiv:cond-mat/0012329 · Physical review. B, Condensed matter

Finite-temperature numerical renormalization group study of the Mott transition

R. Bulla, Theo A. Costi, D. Vollhardt

Published Jun 28, 2001• 281 citations

arXiv HTML PDF

Abstract

T<{T}_{\mathrm{c}}\ensuremath{\approx}0.02W

(W:

bandwidth) we find hysteresis with first-order transitions both at

{U}_{\mathrm{c}1}

(defining the insulator to metal transition) and at

{U}_{\mathrm{c}2}

(defining the metal to insulator transition), at

T>{T}_{\mathrm{c}}

there is a smooth crossover from metalliclike to insulatinglike solutions.

DOI: 10.1103/physrevb.64.045103

Related papers

Zero Temperature Metal-Insulator Transition in the Infinite-Dimensional Hubbard Model

R. Bulla

The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands.The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands.

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Gun Sang Jeon, Tae-Ho Park, Jung Hoon Han +2 more

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 $U$ or $g$ 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.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 $U$ or $g$ 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.

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

T<{T}_{\mathrm{c}}\ensuremath{\approx}0.02W

(W:

bandwidth) we find hysteresis with first-order transitions both at

{U}_{\mathrm{c}1}

(defining the insulator to metal transition) and at

{U}_{\mathrm{c}2}

(defining the metal to insulator transition), at

T>{T}_{\mathrm{c}}

there is a smooth crossover from metalliclike to insulatinglike solutions.

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}

U

---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.

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.