A nucleon-nucleon chiral potential with a corrective density dependent term simulating a three-body force is used in a self-consistent calculation of the dipole strength distribution in neutron-rich nuclei, with special attention to the low-lying spectra associated to the pygmy resonance. A Hartree-Fock-Bogoliubov basis is generated and adopted in Tamm-Dancoff and random-phase approximations and, then, in an equation of motion approach which includes a basis of two-phonon states.
The direct use of the mentioned chiral potential improves the description of both giant and pygmy dipole modes with respect to other realistic interactions. Moreover, the inclusion of the two-phonon states induces a pronounced fragmentation of the giant resonance and enhances the density of the low-lying levels in the pygmy region in agreement with recent experiments.