In a major paper in Science, Perimeter Faculty member Xiao-Gang Wen
reveals a modern reclassification of all 500 phases of matter. 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 paper
provides a revealing look at the intricate and fascinating world of quantum entanglement, and an important step toward a modern reclassification of all phases of matter.
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
"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. When two particles are
entangled, certain measurements performed on one of them immediately
affect the other, no matter how far apart the particles are. The
patterns of such quantum effects, unlike the patterns of the atomic positions, could not be described by their symmetries.
If you were to describe a city as a topologically ordered
state from the cockpit of your impossibly tiny ship, you'd no longer be
describing the girders and buildings of the crystals you passed, but
rather invisible connections between them – rather like describing a
city based on the information flow in its telephone system. This more
general description of matter developed by Wen and collaborators was
powerful – but there were still a few phases that didn't fit.
Specifically, there were a set of short-range entangled phases that did
not break the symmetry, the so-called symmetry-protected topological
phases.
Examples of symmetry-protected phases include some topological
superconductors and topological insulators, which are of widespread
immediate interest because they show promise for use in the coming first
generation of quantum electronics. In the paper featured in today's
issue of Science, Wen and collaborators reveal a new system which can,
at last, successfully classify these symmetry-protected phases.
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.
For more information: Science paper:
www.sciencemag.org/content/338/6114/1604.full The current issue of
Nature provides experimental confirmation of the existence of quantum
spin liquids, one of the new states of matter that was theoretically
predicted by Wen and collaborators Wen's essay on the connections
between condensed matter physics and cosmology An introduction to understanding phases of matter based on symmetry Journal reference: Science Nature
Source: The Daily Galaxy via Perimeter Institute for Theoretical Physics
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