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We investigate in this paper time-dependent non-Hermitian Hamiltonians, whichconsist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian isPT symmetric but the latter one is not. A time-dependent non-unitary operatoris proposed to construct the non-Hermitian invariant, which is verified aspseudo-Hermitian with real eigenvalues. The exact solutions are obtained interms of the eigenstates of the pseudo-Hermitian invariant operator for boththe 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. Theanalytical results are exactly in agreement with those of correspondingHermitian Hamiltonians in the literature.

Non-Hermitian Hamiltonian beyond PT-symmetry for time-dependant SU(1,1)  and SU(2) systems -- exact solution and geometric phase in pseudo-invariant  theory