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Interacting topological insulators in three dimensions: classification and properties

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A fundamental
open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence
of strong electron interactions. In this talk I describe recent work
showing that there are 6 new electronic topological insulators that have
no non-interacting counterpart. Combined with the previously known
band-insulators, these produce a total of 8 topologically distinct
phases. Two of the new topological insulators have a simple physical
description as Mott insulators in which the electron spins form spin
analogs of the familiar topological band-insulator. The remaining are
obtained as combinations of these two `topological paramagnets' and the
topological band insulator. These 8 phases form a complete list of all
possible interacting topological insulators, and are classified by a
$\mathbb{Z}_2^3$ group-structure.
As a necessary part of the talk I will also review progress in the
theory of bosonic Symmetry Protected Topological phases in 3d.