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The interplay of symmetry and topology in quantum condensed matter

Lukasz Fidkowski, Stony Brook
Monday, January 23, 2017 - 4:00pm to 5:00pm
PAT C-520
Many quantum phases of matter can be understood on the basis
of symmetry. For example, the universal properties magnets, crystals,
and even superfluids are a consequence of their spontaneous breaking of
rotational, translational, and charge conservation symmetries,
respectively. The fractional quantum Hall effect, discovered in 1982,
is the first striking example of a phase that transcends this symmetry
breaking framework, and instead exhibits a non-local `topological’
order, which does not rely on symmetry at all, but instead is
characterized by emergent fractionalized excitations and chiral edge
modes. More recently, with the discovery of topological insulators, it
has been realized that in general, the interplay between symmetry and
topology is more subtle, and a much richer phenomenology than previously
thought can result. In this talk, I will discuss the new `symmetry
protected’ and `symmetry enriched’ topological orders that can arise in
this way, including their theoretical classification and potential
physical signatures. I will also discuss exotic strongly interacting
surface states that are available to such systems, and their connections
to anomalies in discrete gauge theories. Finally, I will also talk
about ongoing work on symmetry protected topological phenomena away from
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