The 500 Phases of Matter: New System Successfully Classifies Symmetry-Protected Phases

Dec. 21, 2012 — Forget solid, liquid, and gas: there are in fact more than 500 phases of matter. In a major paper in a recent issue of Science, Perimeter Faculty member Xiao-Gang Wen reveals a modern reclassification of all of them.

Condensed matter physics -- the branch of physics responsible for discovering and describing most of these phases -- has traditionally classified phases by the way their fundamental building blocks -- usually atoms -- are arranged. The key is something called symmetry.

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Beginning in the 1980s, condensed matter researchers, including Xiao-Gang Wen -- now a faculty member at Perimeter Institute -- investigated new quantum systems where numerous ground states existed with the same symmetry. Wen pointed out that those new states contain a new kind of order: topological order. Topological order is a quantum mechanical phenomenon: it is not related to the symmetry of the ground state, but instead to the global properties of the ground state's wave function. Therefore, it transcends the Landau paradigm, which is based on classical physics concepts.

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Using modern mathematics -- specifically group cohomology theory and group super-cohomology theory -- the researchers have constructed and classified the symmetry-protected phases in any number of dimensions and for any symmetries. Their new classification system will provide insight about these quantum phases of matter, which may in turn increase our ability to design states of matter for use in superconductors or quantum computers.