Physical Review Letters

Hall Coefficient for the Two-Dimensional Hubbard Model

Fakher F. Assaad, Masatoshi Imada

Published May 8, 1995• 41 citations

Abstract

We calculate with quantum Monte Carlo methods the Hall coefficient ${R}_{H}$ for the 2D Hubbard model at small hole doping near half filling. In the weak coupling regime ${R}_{H}$ is electronlike. In the strong coupling regime, where the mapping to the $t$- $J$ model is justified, ${R}_{H}$ is electronlike with small amplitude in the temperature regime $T>U$, $T<J$ and holelike in the temperature regime $J<T<U$. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers.

DOI: 10.1103/physrevlett.74.3868

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Physical Review Letters

Hall Coefficient for the Two-Dimensional Hubbard Model

Fakher F. Assaad, Masatoshi Imada

Published May 8, 1995• 41 citations

Publisher

Abstract

We calculate with quantum Monte Carlo methods the Hall coefficient

{R}_{H}

for the 2D Hubbard model at small hole doping near half filling. In the weak coupling regime

{R}_{H}

is electronlike. In the strong coupling regime, where the mapping to the

t

J

model is justified,

{R}_{H}

is electronlike with small amplitude in the temperature regime

T>U

T<J

and holelike in the temperature regime

J<T<U

. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers.

DOI: 10.1103/physrevlett.74.3868

Related papers

Hall conductivity and Fermi surface in highly correlated systems

Horacio E. Castillo, C. A. Balseiro

Physical Review LettersJan 6, 199234 citations

Two-Dimensional Hubbard Model –Metal Insulator Transition Studied by Monte Carlo Calculation–

Nobuo Furukawa, Masatoshi Imada

The Hubbard model on a square lattice in the ground state is investigated. Various aspects of Mott transition at half-filling are clarified from the quantum Monte Carlo study. Critical exponents of the transition for charge and spin correlations are estimated. For the doping concentration δ, the charge susceptibility is proportional to δ -1 indicating the divergence of charge mass for δ→0, while the spin susceptibility is always finite and not singular near δ=0. Several theoretical consequences of the above results are discussed. Incommensurate peak amplitude of spin correlation scales as (δ-δ c ) -1 with δ c <0.01 in disagreement with RPA results ln (δ-δ c ). The antiferromagnetic order at the half-filling also shows strong correlation character and is not sensitive to the shape of the fermi surface, while the incommensurate peak observed away from the half-filling is sensitively suppressed by the loss of partial nesting consistently with the weak coupling picture. Comparisons with experimental indications of high- T c oxides are made.The Hubbard model on a square lattice in the ground state is investigated. Various aspects of Mott transition at half-filling are clarified from the quantum Monte Carlo study. Critical exponents of the transition for charge and spin correlations are estimated. For the doping concentration δ, the charge susceptibility is proportional to δ -1 indicating the divergence of charge mass for δ→0, while the spin susceptibility is always finite and not singular near δ=0. Several theoretical consequences of the above results are discussed. Incommensurate peak amplitude of spin correlation scales as (δ-δ c ) -1 with δ c <0.01 in disagreement with RPA results ln (δ-δ c ). The antiferromagnetic order at the half-filling also shows strong correlation character and is not sensitive to the shape of the fermi surface, while the incommensurate peak observed away from the half-filling is sensitively suppressed by the loss of partial nesting consistently with the weak coupling picture. Comparisons with experimental indications of high- T c oxides are made.

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Ilia Khait, Sauri Bhattacharyya, Abhisek Samanta +1 more

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npj Quantum MaterialsDec 16, 20239 citations

We calculate with quantum Monte Carlo methods the Hall coefficient

{R}_{H}

for the 2D Hubbard model at small hole doping near half filling. In the weak coupling regime

{R}_{H}

is electronlike. In the strong coupling regime, where the mapping to the

t

J

model is justified,

{R}_{H}

is electronlike with small amplitude in the temperature regime

T>U

T<J

and holelike in the temperature regime

J<T<U

. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers.

We compute the (zero frequency) Hall coefficient

R_H

, and the high frequency Hall constant

R_H^*

for the strong coupling Hubbard model away from half-filling, in the

d=\infty

/ local approximation, using the new iterated perturbation scheme proposed by Kajueter and Kotliar. We find quantitative agreement of our

R_H^*

with the QMC results obtained in two dimensions by Assaad and Imada [Phys. Rev. Lett. {\bf 74}, 3868 (1995)]. However while the {\it sign} of

R_H

is quite accurately reproduced by

R_H^*

the doping dependence of its magnitude at large U is not. We report results for the complete temperature

(T)

, doping

(x)

and

U

dependence of

R_H

and

R_H^*

and discuss their possible relevance to doped cuprates.

We study the temperature and doping dependence of the two-dimensional (2D) Hubbard model in the intermediate coupling regime

(U=4).

As temperature is decreased for a half-filled band, 2D critical spin fluctuations give rise to a strong local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({k}_{F},\ensuremath{\omega})|$ at $\ensuremath{\omega}=0,$ leading to a split peak in the spectral function. These strong fluctuations dominating near half filling are completely destroyed by 12% doping concentration. Below this concentration the imaginary part of the self-energy vanishes nearly quadratically in frequency at the Fermi energy, a Fermi-liquid-like feature. With varying the temperature at this concentration, we present numerical evidence for the band Kondo effect in the doped 2D Hubbard model by showing at low temperatures a growing peak in the density of states, nearly quadratically vanishing (in frequency) scattering rates at the Fermi energy and a linearly vanishing (in temperature) effective magnetic moment.