  We study a one-dimensional system that consists of an electron gas coupled to
a spin-1/2 chain by Kondo interaction away from half-filling. We show that
zero-temperature transitions between phases with "small" and "large" Fermi
momenta can be continuous. Such a continuous but Fermi-momentum-changing
transition arises in the presence of spin anisotropy, from a Luttinger liquid
with a small Fermi momentum to a Kondo-dimer phase with a large Fermi momentum.
We have also added a frustrating next-nearest-neighbor interaction in the spin
chain to show the possibility of a similar Fermi-momentum-changing transition,
between the Kondo phase and a spin-Peierls phase, in the spin isotropic case.
This transition, however, appears to involve a region in which the two phases
coexist.
