  We investigate in this paper time-dependent non-Hermitian Hamiltonians, which
consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is
PT symmetric but the latter one is not. A time-dependent non-unitary operator
is proposed to construct the non-Hermitian invariant, which is verified as
pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in
terms of the eigenstates of the pseudo-Hermitian invariant operator for both
the SU(1,1)and SU(2)systems in a unified manner. Then, we derive the LR phase,
which can be separated to the dynamic phase and the geometrical phase. The
analytical results are exactly in agreement with those of corresponding
Hermitian Hamiltonians in the literature.
