  Many quantum condensed-matter systems, and probably the quantum vacuum of our
Universe, are strongly correlated and strongly interacting fermionic systems,
which cannot be treated perturbatively. However, physics which emerges in the
low-energy does not depend on the complicated details of the system and is
relatively simple. It is determined by the nodes in the fermionic spectrum,
which are protected by topology in momentum space (in some cases, in
combination with the vacuum symmetry). Here we illustrate this universality on
some examples of quantum phase transitions, which can occur between the vacua
with the same symmetry but with diferent topology in momentum space. The
quantum phase transitions between the fully gapped states with different
momentum-space topology are also discussed.
