We review the leading momentum, frequency, and temperature dependences of the single-particle self-energy and the corresponding term in the entropy of a two-dimensional Fermi liquid (FL) with a free-particle spectrum. We calculate the corrections to these leading dependences for the paramagnon model and the electron gas and find that the leading dependences are limited to regions of energy and temperature which decrease with decreasing number density of fermions. This can make it difficult to identify the frequency- and temperature-dependent characteristics of a FL ground state in experimental quantities in low-density systems even when complications of band structure and other degrees of freedom are absent. This is an important consideration when the normal-state properties of the undoped cuprate superconductors are analyzed.We review the leading momentum, frequency, and temperature dependences of the single-particle self-energy and the corresponding term in the entropy of a two-dimensional Fermi liquid (FL) with a free-particle spectrum. We calculate the corrections to these leading dependences for the paramagnon model and the electron gas and find that the leading dependences are limited to regions of energy and temperature which decrease with decreasing number density of fermions. This can make it difficult to identify the frequency- and temperature-dependent characteristics of a FL ground state in experimental quantities in low-density systems even when complications of band structure and other degrees of freedom are absent. This is an important consideration when the normal-state properties of the undoped cuprate superconductors are analyzed.

arXiv:cond-mat/9705065Physical review. B, Condensed matterJan 1, 19983 citations

Electron correlation in a two-dimensional quantum electron liquid

J. S. Thakur

Solid State CommunicationsJan 1, 19860 citations

Ground-state properties of the one dimensional electron liquid

Reza Asgari

arXiv:cond-mat/0703359Solid State CommunicationsDec 21, 20067 citations

Green’s-function self-energies in the two-dimensional Holstein model

R. M. Noack, Douglas J. Scalapino

We examine the behavior of the electron and phonon self-energies obtained from quantum Monte Carlo simulations of the two-dimensional Holstein model as a function of Matsubara frequency and momentum. For the half-filled system, there is a finite-temperature phase transition to an insulating charge-density-wave state, and the electron self-energy develops a distinctive divergence. The renormalized phonon frequency softens strongly with temperature at the commensurate wave vector. Away from half-filling, the electron self-energy behaves in a manner consistent with that of a Fermi liquid.We examine the behavior of the electron and phonon self-energies obtained from quantum Monte Carlo simulations of the two-dimensional Holstein model as a function of Matsubara frequency and momentum. For the half-filled system, there is a finite-temperature phase transition to an insulating charge-density-wave state, and the electron self-energy develops a distinctive divergence. The renormalized phonon frequency softens strongly with temperature at the commensurate wave vector. Away from half-filling, the electron self-energy behaves in a manner consistent with that of a Fermi liquid.

Physical review. B, Condensed matterJan 1, 199328 citations

Quasiparticles in Two-Dimensional Hubbard Model: Splitting of Spectral Weight

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

Self-energy contributions to the dynamic structure factor of an electron liquid

Göran Niklasson

Solid State CommunicationsMay 1, 19856 citations

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.