500 new phases of matter based on quantum physics defined

In a recent paper in Science , some physicists successfully place a system which can classify symmetry protected phases. Physicists have classifed matter in new kind of order called topology rather than the classical model. 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.

Traditionally the matter has been classified as solid, liquid, gases and plasma based on the symmetry of the material. For example, going through the crystals of liquid water, one would see the same amount of atoms coming from top,
bottom and sides. That is, the liquid is highly symmetric. 

However going through solid ice, you would see the straight rows of crystalline structures passing. Certain angles would give you different views. Certain paths would be blocked, others wide open. Ice has many symmetries – for instance every layer would look the same- but physicists would say ice has lower symmetry. This approach for classifying the matter is known as Landau paradigm. It was a sound theory given by Landau and it was widely supported. That's why it was such an eye-opening experience when they discovered a handful of phases that Landau couldn't describe.

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, making the number of phases more than 500. 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 .

More info on Science