arXiv:cond-mat/9902290 · Physical Review Letters

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

R. Bulla

Published Jul 5, 1999• 321 citations

Abstract

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.

DOI: 10.1103/physrevlett.83.136

Related papers

Finite-temperature numerical renormalization group study of the Mott transition

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

arXiv:cond-mat/0012329Physical review. B, Condensed matterJun 28, 2001281 citations

Dynamical density-matrix renormalization group for the Mott–Hubbard insulator in high dimensions

Satoshi Nishimoto, Florian Gebhard, Eric Jeckelmann

arXiv:cond-mat/0406666Journal of Physics Condensed MatterSep 21, 200461 citations

Numerical renormalization group calculations for the self-energy of the impurity Anderson model

R. Bulla, Alex C. Hewson, Thomas Pruschke

arXiv:cond-mat/9804224Journal of Physics Condensed MatterSep 21, 1998288 citations

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

E. Z. Kuchinskii, I. A. Nekrasov, M. V. Sadovskii

arXiv:0706.2618Journal of Experimental and Theoretical PhysicsMar 1, 200824 citations

Dynamical mean-field theory of the Hubbard-Holstein model at half filling: Zero temperature metal-insulator and insulator-insulator transitions

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

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

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

É. Z. Kuchinskiǐ, N. A. Kuleeva, I. A. Nekrasov +1 more

arXiv:0908.3747Journal of Experimental and Theoretical PhysicsFeb 1, 201014 citations

arXiv:cond-mat/9902290 · Physical Review Letters

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

R. Bulla

Published Jul 5, 1999• 321 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.83.136

Related papers

Finite-temperature numerical renormalization group study of the Mott transition

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

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.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.

arXiv:cond-mat/0012329Physical review. B, Condensed matterJun 28, 2001281 citations

Dynamical density-matrix renormalization group for the Mott–Hubbard insulator in high dimensions

Satoshi Nishimoto, Florian Gebhard, Eric Jeckelmann

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ 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 model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ 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 $U_{\rm c}$.

arXiv:cond-mat/0406666Journal of Physics Condensed MatterSep 21, 200461 citations

Numerical renormalization group calculations for the self-energy of the impurity Anderson model

R. Bulla, Alex C. Hewson, Thomas Pruschke

We present a new method for calculating directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical renormalization group method by writing this quantity as the ratio of two correlation functions. This way of calculating turns out to be considerably more reliable and accurate than that via the impurity Green's function alone. We give results for the self-energy for the case of a constant coupling between the impurity and the conduction band and the effective arising in the dynamical mean-field theory of the Hubbard model. The implications of the problem of the metal-insulator transition in the Hubbard model are also discussed.We present a new method for calculating directly the one-particle self-energy of an impurity Anderson model with Wilson's numerical renormalization group method by writing this quantity as the ratio of two correlation functions. This way of calculating turns out to be considerably more reliable and accurate than that via the impurity Green's function alone. We give results for the self-energy for the case of a constant coupling between the impurity and the conduction band and the effective arising in the dynamical mean-field theory of the Hubbard model. The implications of the problem of the metal-insulator transition in the Hubbard model are also discussed.

arXiv:cond-mat/9804224Journal of Physics Condensed MatterSep 21, 1998288 citations

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

E. Z. Kuchinskii, I. A. Nekrasov, M. V. Sadovskii

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.

arXiv:0706.2618Journal of Experimental and Theoretical PhysicsMar 1, 200824 citations

Dynamical mean-field theory of the Hubbard-Holstein model at half filling: Zero temperature metal-insulator and insulator-insulator transitions

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

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

É. Z. Kuchinskiǐ, N. A. Kuleeva, I. A. Nekrasov +1 more

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.

arXiv:0908.3747Journal of Experimental and Theoretical PhysicsFeb 1, 201014 citations

(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}

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.