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Symmetry Protected Topological Phases; from Quantum Entanglement to Interaction Effects

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I will briefly review topological phases of non
interacting fermions, such as topological insulators, and discuss how ideas
from quantum information, in particular the entanglement spectrum, can be used
to characterize them.

For topological phases protected by inversion symmetry I
argue that this is the ideal tool, and discuss how it leads to a classification
of 3D topological phases. Next, I will discuss topological phases that only
appear in the presence of interactions, although they share essential
characteristics with non-interacting topological phases. A general theory of
such states of bosons in 2+1 dimensions will be given, and specific examples,
the bosonic analogs of topological superconductors and insulators, will be