Progress of Theoretical Physics

Quasiparticle Weight of the Two-Dimensional Hubbard Model in thet-Matrix Approximation

Osamu Narikiyo

Published Jun 1, 1997• 1 citation

Abstract

The quasiparticle weight of the two-dimensional Hubbard model in thet-matrix approximation is discussed in comparison with a recent report by Yokoyama and Fukuyama (J. Phys. Soc. Jpn. 66 (1997), 529) where the breakdown of the quasiparticle description of the Fermi liquid was concluded.

DOI: 10.1143/ptp.97.1019

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Progress of Theoretical Physics

Quasiparticle Weight of the Two-Dimensional Hubbard Model in thet-Matrix Approximation

Osamu Narikiyo

Published Jun 1, 1997• 1 citation

Publisher

Abstract

DOI: 10.1143/ptp.97.1019

Related papers

One-Particle Spectral Weightof the Two-Dimensional Hubbard Modelin thet-Matrix Approximation

Osamu Narikiyo, Kazumasa Miyake

Journal of the Physical Society of JapanJul 15, 19954 citations

Breakdown of the quasiparticle picture in the low-density limit of the one-dimensional Hubbard model

Shaojin Qin, Tiezheng Qian, Lu Yu +1 more

Using the finite-size scaling of results obtained by exact diagonalization, we study the low-density limit of the one-dimensional Hubbard model. Calculating the quasiparticle weight, we demonstrate that for a given particle number N and system size L, there always exists a crossover point ${\mathit{U}}_{\mathit{c}}$ separating the Fermi-liquid (U ${\mathit{U}}_{\mathit{c}}$ ) and non-Fermi-liquid (U> ${\mathit{U}}_{\mathit{c}}$ ) regimes (U is the Hubbard repulsion). We find that for a fixed N, ${\mathit{U}}_{\mathit{c}}$ is inversely proportional to L, keeping ${\mathit{U}}_{\mathit{c}}$ L/t constant (with t as the hopping integral), as L is large enough. It follows that in the low-density (in fact vanishing density) limit L\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathit{U}}_{\mathit{c}}$ \ensuremath{\rightarrow}0, so the system is always in the non-Fermi-liquid regime as long as U>0. We show that our numerical results are consistent with the Bethe-ansatz solution.Using the finite-size scaling of results obtained by exact diagonalization, we study the low-density limit of the one-dimensional Hubbard model. Calculating the quasiparticle weight, we demonstrate that for a given particle number N and system size L, there always exists a crossover point ${\mathit{U}}_{\mathit{c}}$ separating the Fermi-liquid (U${\mathit{U}}_{\mathit{c}}$) and non-Fermi-liquid (U>${\mathit{U}}_{\mathit{c}}$) regimes (U is the Hubbard repulsion). We find that for a fixed N, ${\mathit{U}}_{\mathit{c}}$ is inversely proportional to L, keeping ${\mathit{U}}_{\mathit{c}}$L/t constant (with t as the hopping integral), as L is large enough. It follows that in the low-density (in fact vanishing density) limit L\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathit{U}}_{\mathit{c}}$\ensuremath{\rightarrow}0, so the system is always in the non-Fermi-liquid regime as long as U>0. We show that our numerical results are consistent with the Bethe-ansatz solution.

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Hidetoshi Fukuyama, Masao Ogata

It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $ Σ(k, \varepsilon + i0) \equiv Σ^{R}(k, \varepsilon) $ are, $ {\rm Im} Σ^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - ξ_{k}|^{- γ(k)} $ where $a$ is some constant, $ξ_{k} = \varepsilon(k)-μ, \varepsilon(k)$ being the band energy, and the critical exponent $ γ(k) $, which depends on the curvature of the Fermi surface at $ k $, satisfies, $ 0 \leq γ(k) \leq 1 $. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $ \varepsilon, ξ_{k} \rightarrow 0 $ but for $ ξ_{k} \neq 0 $ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $ Σ(k, \varepsilon + i0) \equiv Σ^{R}(k, \varepsilon) $ are, $ {\rm Im} Σ^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - ξ_{k}|^{- γ(k)} $ where $a$ is some constant, $ξ_{k} = \varepsilon(k)-μ, \varepsilon(k)$ being the band energy, and the critical exponent $ γ(k) $, which depends on the curvature of the Fermi surface at $ k $, satisfies, $ 0 \leq γ(k) \leq 1 $. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $ \varepsilon, ξ_{k} \rightarrow 0 $ but for $ ξ_{k} \neq 0 $ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.

arXiv:cond-mat/9409044Journal of the Physical Society of JapanNov 15, 199421 citations

{\mathit{U}}_{\mathit{c}}

separating the Fermi-liquid (U

{\mathit{U}}_{\mathit{c}}

) and non-Fermi-liquid (U>

{\mathit{U}}_{\mathit{c}}

) regimes (U is the Hubbard repulsion). We find that for a fixed N,

{\mathit{U}}_{\mathit{c}}

is inversely proportional to L, keeping

{\mathit{U}}_{\mathit{c}}

L/t constant (with t as the hopping integral), as L is large enough. It follows that in the low-density (in fact vanishing density) limit L\ensuremath{\rightarrow}\ensuremath{\infty},

{\mathit{U}}_{\mathit{c}}

\ensuremath{\rightarrow}0, so the system is always in the non-Fermi-liquid regime as long as U>0. We show that our numerical results are consistent with the Bethe-ansatz solution.

It is shown that the energy

(\varepsilon)

and momentum

(k)

dependences of the electron self-energy function $ Σ(k, \varepsilon + i0) \equiv Σ^{R}(k, \varepsilon) $ are, $ {\rm Im} Σ^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - ξ_{k}|^{- γ(k)} $ where

a

is some constant,

ξ_{k} = \varepsilon(k)-μ, \varepsilon(k)

being the band energy, and the critical exponent $ γ(k) $, which depends on the curvature of the Fermi surface at $ k $, satisfies, $ 0 \leq γ(k) \leq 1 $. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $ \varepsilon, ξ_{k} \rightarrow 0 $ but for $ ξ_{k} \neq 0 $ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.