Tag Archives: Xiao-Gang Wen

500 phases of matter take us beyond solid, liquid, and gas

A Dec. 22, 2012 news item on Nanowerk touts a major reclassification and expansion of the states of matter,

Forget solid, liquid, and gas: there are in fact more than 500 phases of matter. In a major paper in Science, Perimeter [Institute] Faculty member Xiao-Gang Wen reveals a modern reclassification of all of them.

Using modern mathematics, Wen and collaborators reveal a new system which can, at last, successfully classify symmetry-protected phases of matter. 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.

The Perimeter Institute for Theoretical Physics, where this work was done, is located in Waterloo, Ontario (Canada). More information about Wen’s latest publication can be found in this Dec. 21, 2012 press release on the Institute website (there are also links to more explanations about condensed matter and other related topics),

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.

To understand symmetry, imagine flying through liquid water in an impossibly tiny ship: the atoms would swirl randomly around you and every direction – whether up, down, or sideways – would be the same. The technical term for this is “symmetry” – and liquids are highly symmetric. Crystal ice, another phase of water, is less symmetric. If you flew through ice in the same way, you would see the straight rows of crystalline structures passing as regularly as the girders of an unfinished skyscraper. Certain angles would give you different views. Certain paths would be blocked, others wide open. Ice has many symmetries – every “floor” and every “room” would look the same, for instance – but physicists would say that the high symmetry of liquid water is broken.

Classifying the phases of matter by describing their symmetries and where and how those symmetries break is known as the Landau paradigm. More than simply a way of arranging the phases of matter into a chart, Landau’s theory is a powerful tool which both guides scientists in discovering new phases of matter and helps them grapple with the behaviours of the known phases. Physicists were so pleased with Landau’s theory that for a long time they believed that all phases of matter could be described by symmetries. That’s why it was such an eye-opening experience when they discovered a handful of phases that Landau couldn’t describe.

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.

Topological order is a more general understanding of quantum phases and the transitions between them. In the new framework, the phases of matter were described not by the patterns of symmetry in the ground state, but by the patterns of a decidedly quantum property – entanglement.

Wen’s new work has been published in latest issue of Science,

Symmetry-Protected Topological Orders in Interacting Bosonic Systems by Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen in Science 21 December 2012: Vol. 338 no. 6114 pp. 1604-1606 DOI: 10.1126/science.1227224

The article is behind a paywall.

Surprisingly, there aren’t any visualizations of the 500 states similar to chemistry’s periodic table to elements; at least, they aren’t included in the press materials on the Institute’s website.