  We have extended the density matrix renormalization group (DMRG) approach to
two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians.
The applications are carried out for three- and four-nucleon (proton-neutron)
systems within the Gamow Shell Model (GSM) in the complex-energy plane. We
study necessary and sufficient conditions for the GSM+DMRG method to yield the
correct ground state eigenvalue and discuss different truncation schemes within
DMRG. The proposed approach will enable configuration interaction studies of
weakly-bound and unbound strongly interacting complex systems which, because of
a prohibitively large size of Fock space, cannot be treated by means of the
direct diagonalization.
