What is the atomic limit? I am attempting to grasp topological superconductivity for an assignment and in trying to understand what makes a quantum system topological have came across the following paragraph;

"In the case of quantum manybody systems, simple combinations of atomic wavefunctions are considered to be trivial, and hence any condensed matter system whose wavefunction is adiabatically connected to the atomic limit is topologically trivial.
  However, when the wavefunction is adiabatically distinct
  from the atomic limit, such a system may be called topological."

Could somebody explain what is meant by this? I'm struggling to find a definition of the atomic limit, so I'm not sure what is meant by talking about a wavefunction in relation to the atomic limit.
 A: Let me please refer you to the article Topological Quantum Chemistry by Bradlyn, Elcoro, Cano, Vergniory, Wang, Felser, Aroyo and Bernevig where the concept of an atomic limit is  defined in detail. (please see also the supplementary material).
The basic definition (modulo some details) is given in the discussion  following definition 1 on page 3:
An atomic limit is a band structure admitting a set of exponentially Localized Wannier functions respecting all the symmetries of the crystal and possibly time reversal.  When the atomic separation  is taken to infinity, these Wannier functions coincide in most cases with localized atomic orbitals. This band structure is characterized by a trivial topology. 
In $\mathbb{Z}_2$  topological insulators, exponentially Localized Wannier functions exist but then they (necessarily) break the time reversal symmetry, (thus conform with the above definition).
There can be multiple atomic limits. The authors note (section V) that the Rice-Mele model can be understood as a system with two nonequivalent atomic limits. Both limits have localized Wannier  functions as required, but in the second one, the Wannier functions are not localized on the atomic  positions, but rather constitute of hybridized  orbitals localized away from the atoms.
Atomic limits are in a one-to one correspondence with the band representations introduced by Zak  and discussed in detail in the supplementary material linked above. Please see also a more qualitative description in the following lecture note by Cano.
