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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON VERY…

Slide 1 Space Group = {Essential Symmetry Operations}  {Bravais Lattice} N = # of translation operations in the Bravais lattice (N is a very large number) h = # of rotation-translations…

Competing instabilities in strongly correlated electron systems Exploring Topological Phases With Quantum Walks $$ NSF, AFOSR MURI, DARPA, ARO Harvard-MIT Takuya Kitagawa,…

Symmetry, Groups and Crystal Structures The Seven Crystal Systems Minerals structures are described in terms of the unit cell The Unit Cell The unit cell of a mineral is…

Symmetry, Groups and Crystal Structures The Seven Crystal Systems Minerals structures are described in terms of the unit cell The Unit Cell The unit cell of a mineral is…

Symmetry, Groups and Crystal Structures The Seven Crystal Systems Minerals structures are described in terms of the unit cell The Unit Cell The unit cell of a mineral is…