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Physical Review A

Electron Gas at Metallic Densities

Gerd E. Keiser, Fa Yueh Wu

Published Dec 1, 1972• 34 citations
Publisher

Abstract

The ground-state properties of an electron gas at metallic densities are investigated using the Wu-Feenberg theory of Fermi liquids. The correlation energy, the low-temperature specific heat, and the spin susceptibility are computed, and the ground state is found to be paramagnetic. The perturbative correction to the correlation energy owing to the particle-hole excitations in a correlated-basis-function formulation is found to be insignificant.

DOI
10.1103/physreva.6.2369

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Journal of Experimental and Theoretical Physics Letters•Oct 1, 2012•15 citations
The ground-state properties of an electron gas at metallic densities are investigated using the Wu-Feenberg theory of Fermi liquids. The correlation energy, the low-temperature specific heat, and the spin susceptibility are computed, and the ground state is found to be paramagnetic. The perturbative correction to the correlation energy owing to the particle-hole excitations in a correlated-basis-function formulation is found to be insignificant.
We study the metal-insulator transition in the highly correlated electron gas, described by the Hubbard Hamiltonian, within a renormalization group approach. The scaling theory of critical phenomena and results associated with the existence of a zero-temperature fixed point are used to derive expressions for the susceptibility and specific heat at very low temperatures. We discuss the enhancement of these quantities in the Fermi liquid due to the proximity of the transition to an insulating state. Finally we compare our results with those expected for the case of a magnetic instability.
An extension of the effective-potential expansion method is made to treat low-lying excited states in an interacting many-electron system. This extension provides a prescription for the microscopic calculation of the Landau's Fermi-liquid parameters. By a systematic evaluation of those parameters for the electron gas at metallic densities, we obtain results for the compressibility that are very close to the exact values. We also obtain the results for the spin susceptibility and the effective mass. Those results are compared with those obtained by other methods.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
We discuss interaction effects for the one-dimensional electron gas with a repulsive \ensuremath{\delta}-function interaction potential by using the random-phase approximation and a local-field correction. Analytical results for the local-field correction of charge-density fluctuations and spin-density fluctuations are obtained. The ground-state energy is found to be in better agreement with the exact result than the ground-state energy calculated within the random-phase approximation. We calculate the pair-correlation functions for electrons with parallel and antiparallel spins and the paramagnetic susceptibility. The energies of the collective density modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q) and the collective spin modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q) are calculated and compared with the energy of the electron-hole excitations ${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q): ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q\ensuremath{\rightarrow}0). The critical exponents for the long-distance behavior of correlation functions are found to be described by local-field corrections. We compare our results for the critical exponents with recent results obtained by bosonization techniques and the conformal field theory.
Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}rs{r}_{s}rs​\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density rs{r}_{s}rs​\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.
The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T ⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T *, appears through a crossover at temperatures T ∼ T * > T ⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T −α with the exponent α }~ 2/3.