  We consider a one-dimensional (1D) two-component atomic Fermi gas with
contact interaction in the even-wave channel (Yang-Gaudin model) and study the
effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within
one of the components. Starting from the microscopic Hamiltonian, we derive an
effective field theory for the spin degrees of freedom using the bosonization
technique. It is shown that at a critical value of the odd-wave interaction
there is a first-order phase transition from a phase with zero total spin and
zero magnetization to the spin-segregated phase where the magnetization locally
differs from zero.
