  The quantum phase transitions in the one-dimensional asymmetric Hubbard model
are investigated with the bosonization approach. The conditions for the phase
transition from density wave to phase separation, the correlation functions and
their exponents are obtained analytically. Our results show that the difference
between the hopping integrals for up- and down-spin electrons is crucial for
the happening of the phase separation. When the difference is large enough, the
phase separation will appear even if the on-site interaction is small.
