Electrical Conductivity of Fermi Liquids. I. Many-body Effect on the Drude Weight
Abstract
On the basis of the Fermi liquid theory, we investigate the many-body effect on the Drude weight. In a lattice system, the Drude weight
D
is modified by electron-electron interaction due to Umklapp processes, while it is not renormalized in a Galilean invariant system. This is explained by showing that the effective mass
m
′
for
D∝n/
m
′
is defined through the current, not velocity, of quasiparticle. It is shown that the inequality
D>0
is required for the stability against the uniform shift of the Fermi surface. The result of perturbation theory applied for the Hubbard model indicates that
D
as a function of the density
n
is qualitatively modified around half filling
n∼1
by Umklapp processes.