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Summary: Topological Phases of Matter
Modeling and Classification
Zhenghan Wang
Microsoft Station Q
RTG in Topology and Geometry, UCSB Oct 21, 2011
Prediction of Quantum Theory
· Quantum computing is possible
· There are non-abelian anyons
Thm: Prediction 2 implies Prediction 1.
Anyon=Localized Non-Local Properties
Favorite Theorems
· Poincare-Hopf Index Thm
· Gauss-Bonnet-Chern Thm
Quantum Systems
· A pair Q=(L, H), where L is a Hilbert space
and H an Hermitian operator, physically H
should be local.
· Examples:
0) L = C2, H= I
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