  The heating of the chromosphere in internetwork regions remains one of the
foremost open questions in solar physics. In the present study we tackle this
old problem by using a very high spatial-resolution simulation of quiet-Sun
conditions performed with radiative MHD numerical models and IRIS observations.
We have expanded a previously existing 3D radiative MHD numerical model of the
solar atmosphere, which included self-consistently locally driven magnetic
amplification in the chromosphere, by adding ambipolar diffusion and
time-dependent non-equilibrium hydrogen ionization to the model. The energy of
the magnetic field is dissipated in the upper chromosphere, providing a large
temperature increase due to ambipolar diffusion and the non-equilibrium
ionization (NEQI). At the same time, we find that adding the ambipolar
diffusion and NEQI in the simulation has a minor impact on the local growth of
the magnetic field in the lower chromosphere and its dynamics. Our comparison
between synthesized Mg II profiles from these high spatial resolution models,
with and without ambipolar diffusion and NEQI, and quiet Sun and coronal hole
observations from IRIS now reveal a better correspondence. The intensity of
profiles is increased and the line cores are slightly broader when ambipolar
diffusion and NEQI effects are included. Therefore, the Mg II profiles are
closer to those observed than in previous models, but some differences still
remain.
