Numerical calculations of quasiparticle dynamics in a Fermi liquid

If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the ${\mathit{T}}^{3}$ lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the ${\mathit{T}}^{3}$lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.

Physical review. B, Condensed matterMay 15, 19951 citation

The structure of quasiparticles in a local Fermi liquid

Izak Snyman

Conduction electrons interacting with a dynamic impurity can give rise to a local Fermi liquid. The latter has the same low energy spectrum as an ideal Fermi gas containing a static impurity. The Fermi liquids's elementary excitations are however not bare electrons. In the vicinity of the impurity, they are dressed by virtual particle-hole pairs. Here we study this dressing. Among other things, we construct a mode-resolved measure of dressing. To evaluate it in position representation, we have to circumvent the limitations of the Numerical Renormalization Group, which discretizes the conduction band logarithmically. We therefore extend Natural Orbital methods, that successfully characterize the ground state, to describe excitations. We demonstrate that the dressing profile shows nontrivial powerlaw decay at large distances. Our Natural Orbital methodology could lay the foundation for calculating the properties of local Fermi liquid quasiparticles in nontrivial geometries such as disordered hosts or mesoscopic devices.Conduction electrons interacting with a dynamic impurity can give rise to a local Fermi liquid. The latter has the same low energy spectrum as an ideal Fermi gas containing a static impurity. The Fermi liquids's elementary excitations are however not bare electrons. In the vicinity of the impurity, they are dressed by virtual particle-hole pairs. Here we study this dressing. Among other things, we construct a mode-resolved measure of dressing. To evaluate it in position representation, we have to circumvent the limitations of the Numerical Renormalization Group, which discretizes the conduction band logarithmically. We therefore extend Natural Orbital methods, that successfully characterize the ground state, to describe excitations. We demonstrate that the dressing profile shows nontrivial powerlaw decay at large distances. Our Natural Orbital methodology could lay the foundation for calculating the properties of local Fermi liquid quasiparticles in nontrivial geometries such as disordered hosts or mesoscopic devices.

arXiv:2308.15576Aug 29, 20230 citations

Quasiparticle scattering in Fermi fluids

Franz Mohling, James C. Rainwater

Journal of Low Temperature PhysicsAug 1, 19758 citations

Low-energy physics of the t−J model in d=∞ using extremely correlated Fermi liquid theory: Cutoff second-order equations

B. Sriram Shastry, Edward Perepelitsky

We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with $J=0$ , using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high- $T$ entropy. The resulting quasiparticle weight $Z$ , the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$ . The present scheme is generalizable to finite dimensions and a nonvanishing $J$ .We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with $J=0$, using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high-$T$ entropy. The resulting quasiparticle weight $Z$, the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$. The present scheme is generalizable to finite dimensions and a nonvanishing $J$.

arXiv:1605.08213Physical review. B./Physical review. BJul 28, 201618 citations

Microscopic calculations for a model Fermi liquid

Stefano Fantoni, Sergio Rosati

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoAug 1, 197641 citations

{\mathit{T}}^{3}

lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.

We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with

J=0

, using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter

1/(2S)

in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high-

T

entropy. The resulting quasiparticle weight

Z

, the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite

T

rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising

T

. The present scheme is generalizable to finite dimensions and a nonvanishing

J