We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation
for N interacting electrons with the energy functional of a mean-field
crystal with a localized defect, obtaining a highly non linear many-body problem. The
physical picture is that the electrons constitute a charge defect in an otherwise perfect
periodic crystal. A remarkable feature of such a system is the possibility to form a bound
state of electrons via their interaction with the polarizable background. We prove first
that a single polaron always binds, i.e. the energy functional has a
minimizer for N = 1. Then we discuss the case of multi-polarons
containing N ≥ 2 electrons. We show that their existence is guaranteed
when certain quantized binding inequalities of HVZ type are satisfied.