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Physical review. B, Condensed matter

Quasiparticle properties of the electron gas at metallic densities in the effective-potential expansion method

Yasutami Takada

Published Mar 1, 1991• 24 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.43.5979

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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.
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We present the microscopic derivation of a quasiparticle pseudo-Hamiltonian for an infinitesimally polarized electron liquid. The Hamiltonian is expressed in terms of suitably defined quasiparticle operators. Our approach is based on a canonical transformation which allows one to replace the bare Coulombic coupling between the interacting electrons with an effective interaction between quasiparticles in which collective charge and spin fluctuations are explicitly accounted for. The relevant matrix elements of the charge and spin-density operators enter our theory via linear-response functions: the charge response, the longitudinal and transverse spin responses, and the mixed charge-spin response. These susceptibilities are in turn expressed in terms of the appropriate many-body local fields. As a consequence our method can be seen as an attempt to satisfactorily include in a self-consistent manner the effects of the vertex corrections associated with charge and spin-fluctuations of the electron liquid. As a result useful expressions for the quasiparticle energy and the effective interaction between two quasiparticles are determined. These can, in turn, be employed in a microscopic determination of the parameters of the Landau theory of the Fermi liquid. The generalization of our results to a multicomponent system is also discussed.
The calculation of the induced spin density of a normal fermion system, such as the electron gas, in the limit of small wave numbers, is carried beyond the random phase approximation (R.P.A.) by the method of canonical transformation so as to include the first non-R.P.A. corrections. An expression for the induced spin density in the same limit, exact to all orders of particle-particle coupling, is then derived by more general methods of many-body perturbation theory. It depends only on the knowledge, to all orders of interparticle coupling, of the effective mass and the forward scattering of quasi-particles at the Fermi surface, and also yields the results of the extended R.P.A. on appropriate expansion. In the limit of zero wave number, the resulting expression for the magnetic susceptibility is found identical with that deduced by Landau from a phenomenological basis and may be regarded as an additional confirmation of the microscopic validity of the theory of the Fermi liquid.
Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.
We generalize the Fermi-liquid theory to NNN component systems with SU(N)\mathrm{SU}(N)SU(N) symmetry. We evaluate the Fermi-liquid parameters, effective mass, compressibility, and spin susceptibilities for a repulsive gas. We emphasize the important role of induced density fluctuations when NNN is large. These fluctuations dramatically modify the properties of the gas, in particular the spin susceptibilities, from mean-field predictions.