  We study two-component (or pseudo-spin-1/2) Bose or Fermi gases in one
dimension, in which particles are convertible between the components. Through
bosonization and numerical analyses of a simple lattice model, we demonstrate
that, in such gases, a strong intercomponent repulsion induces spontaneous
population imbalance between the components, namely, the ferromagnetism of the
pseudo spins. The imbalanced phase contains gapless charge excitations
characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We
uncover a crucial effect of the intercomponent particle hopping on the
transition to the imbalanced phase. In the absence of this hopping, the
transition is of first order. At the transition point, the energy spectrum
reveals certain degeneracy indicative of an emergent SU(2) symmetry. With an
infinitesimal intercomponent hopping, the transition becomes of Ising type. We
determine the phase diagram of the model accurately and test the reliability of
the weak-coupling bosonization formalism.
