  The 16 Cyg system is composed of two solar analogs with similar masses and
ages. A red dwarf is in orbit around 16 Cyg A whereas 16 Cyg B hosts a giant
planet. The abundances of heavy elements are similar in the two stars but
lithium is much more depleted in 16 Cyg B that in 16 Cyg A, by a factor of at
least 4.7. The interest of studying the 16 Cyg system is that the two star have
the same age and the same initial composition. The presently observed
differences must be due to their different evolution, related to the fact that
one of them hosts a planet contrary to the other one. We computed models of the
two stars which precisely fit the observed seismic frequencies. We used the
Toulouse Geneva Evolution Code (TGEC) that includes complete atomic diffusion
(including radiative accelerations). We compared the predicted surface
abundances with the spectroscopic observations and confirmed that another
mixing process is needed. We then included the effect of accretion-induced
fingering convection. The accretion of planetary matter does not change the
metal abundances but leads to lithium destruction which depends on the accreted
mass. A fraction of earth mass is enough to explain the lithium surface
abundances of 16 Cyg B. We also checked the beryllium abundances. In the case
of accretion of heavy matter onto stellar surfaces, the accreted heavy elements
do not remain in the outer convective zones but they are mixed downwards by
fingering convection induced by the unstable $\mu$-gradient. Depending on the
accreted mass, this mixing process may transport lithium down to its nuclear
destruction layers and lead to an extra lithium depletion at the surface. A
fraction of earth mass is enough to explain a lithium ratio of 4.7 in the 16
Cyg system. In this case beryllium is not destroyed. Such a process may be
frequent in planet host stars and should be studied in other cases in the
future.
