[1]
http://www.newscientist.com/article.ns?id=mg19325954.200&feedId=fundamentals_rss20
ZnCu3(OH)6Cl2
A new state of matter?
" ...unusual because its electrons are arranged in a
triangular lattice. Normally, electrons prefer to line up so
that their spins are in the opposite direction to that of
their immediate neighbours, but in a triangle this is
impossible - there will always be neighbouring electrons
spinning in the same direction. Wen and his colleagues propose
that such a system would be a string-net liquid. "
From wikipedia: String-net liquid is the phrase used for a
hypothetical state of matter in which the atoms do not line up
in opposing "spins", but in a more erratic order, as if they had
partial spins or charges. Herbertsmithite, a crystalline
material occurring in nature, may have such qualities.
Discovered by Xiao-Gang at the Massachusetts Institute of
Technology. First thought of in 1983.
" Suddenly we realised, maybe the vacuum of our whole universe
is a string-net liquid, "
From: [2]
http://en.wikipedia.org/wiki/Kagome_lattice
" Some minerals, namely jarosites and herbertsmithite, contain
layers with kagome lattice arrangement of atoms in their
crystal structure. These minerals display novel physical
properties connected with geometrically frustrated magnetism.
The term is much in use nowadays in the scientific literature,
especially by theorists studying the magnetic properties of a
theoretical kagome lattice in two or three dimensions. =======
New Scientist published an [3]article about string-net theory
and unification of light and electrons. The following is my
modification of the article trying to make it more accurate.
-- Xiao-Gang Wen [4][IMG]
The universe is a string-net liquid
A mysterious green crystal may be challenging our most basic ideas
about matter and even space-time itself
Zeeya Merali
(March 15, 2007) In 1998, just after he won a share of the
Nobel prize for physics, Robert Laughlin of Stanford
University in California was asked how his discovery of
"particles" with fractional charge would affect the lives of
ordinary people. "It probably won't," he said, "unless people
are concerned about how the universe works." Well, people
were. Xiao-Gang Wen at the Massachusetts Institute of
Technology and Michael Levin at Harvard University ran with
Laughlin's ideas and have come up with a theory for a new
state of matter, and even a tantalizing picture of the nature
of spacetime itself. Levin presented their work at the
Topological Quantum Computing conference at the University of
California, Los Angeles, early this month. The first hint that
a new type of matter may exist came in 1982. "Twenty five
years ago we thought we understood everything about phases and
phase transitions of matter," says Wen. "Then along came an
experiment that opened up a whole new world." "The positions
of electrons in a FQH state appear random like in a liquid,
but they dance around each other in a well organized manner
and form a global dancing pattern." In the experiment,
electrons moving in the interface between two semiconductors
form a strange state, which allows a particle-like excitation
(called a quasiparticle) that carries only 1/3 of electron
charge. Such an excitation cannot be view as a motion of a
single electron or any cluster with finite electrons. Thus
this so-called fractional quantum Hall (FQH) state suggested
that the quasiparticle excitation in a state can be very
different from the underlying particle that form the state.
The quasiparticle may even behave like a fraction of the
underlying particle, even though the underlying particle can
never break apart. It soon became clear that electrons under
certain conditions can organize in a way such that a defect or
a twist in the organization gives rise to a quasiparticle with
fractional charge -- an explanation that earned Laughlin,
Horst St*rmer and Daniel Tsui the Nobel prize (New Scientist,
31 January 1998, p 36). Wen suspected that the effect could be
an example of a new type of matter. Different phases of matter
are characterized by the way their atoms are organized. In a
liquid, for instance, atoms are randomly distributed, whereas
atoms in a solid are rigidly positioned in a lattice. FQH
systems are different. "If you take a snapshot of the position
of electrons in a FQH state they appear random and you think
you have a liquid," says Wen. "But if you follow the motion of
the electrons, you see that, unlike in a liquid, the electrons
dance around each other in a well organized manner and form a
global dancing pattern." It is as if the electrons are
entangled. Today, physicists use the term to describe a
property in quantum mechanics in which particles can be linked
despite being separated by great distances. Wen speculated
that FQH systems represented a state of matter in which
long-range entanglement was a key intrinsic property, with
particles tied to each other in a complicated manner across
the entire material. Different entanglement patterns or
dancing patterns, such as "waltz", "square dance", "contra
dance", etc, give rise to different quantum Hall states.
According to this point of view, a new pattern of entanglement
will lead to a new state of matter. This led Wen and Levin to
the idea that there may be a different way of thinking about
states (or phases) of matter. In an attempt of construct
states will all possible patterns of entanglement, they
formulated a model in which particles form strings and such
strings are free to move "like noodles in a soup" and weave
together into "string-nets" that fill the space. They found
that liquid states of string-nets can realize a huge class of
different entanglement patterns which, in turn, correspond to
a huge class of new states of matter.
Light and matter unified
"What if electrons were not elementary, but were the ends of
long strings in a string-net liquid which becomes our space?"
A state or a phase correspond to an organization of particles.
A deformation in the organization represents a wave in the
state. A new state of matter will usually support new kind of
waves. Wen and Levin found that, in a state of string-net
liquid, the motion of string-nets correspond to a wave that
behaved according to a very famous set of equations --
Maxwell's equations! The equations describe the behavior of
light -- a wave of electric and magnetic field. "A hundred and
fifty years after Maxwell wrote them down, ether -- a medium
that produces those equations -- was finally found." says Wen.
That wasn't all. They found that the ends of strings are
sources of the electric field in the Maxwell's equations. In
other words, the ends of strings behave like charged
electrons. The string-end picture can even reproduce the Fermi
statistics and the Dirac equation that describes the motion of
the electrons. They also found that string-net theory
naturally gave rise to other elementary particles, such as
quarks, which make up protons and neutrons, and the particles
responsible for some of the fundamental forces, such as gluons
and the W and Z bosons. From this, the researchers made
another leap. Could the entire universe be modeled in a
similar way? "Suddenly we realized, maybe the vacuum of our
whole universe is a string-net liquid," says Wen. "It would
provide a unified explanation of how both light and matter
arise." So in their theory elementary particles are not the
fundamental building blocks of matter. Instead, they emerge as
defects or "whirlpools" in the deeper organized structure of
space-time. Here we view our space as a lattice spin system --
the most generic system with local degrees of freedom. There
is no "empty" space and spins are not placed in an empty
space. Without the spins there will be no space and it is the
degrees of freedom of the spins that make the space to exist.
What we regard as the "empty space" corresponds to the ground
state of the spin system. The collective excitations above the
ground state correspond to the elementary particles. But not
long ago, this point of view of elementary particles was not
regarded as a valid approach, since we cannot find any
organization of spins that produce light wave (which leads to
photons) and electron wave (which leads to electrons). Now
this problem is solved. If the spins that form our space
organize into a string-net liquid, then the collective motions
of strings give rise to light waves and the ends of strings
give rise to electrons. The next challenge is to find an
organization of spins that can give rise to gravitational
wave. "Wen and Levin's theory is really beautiful stuff," says
Michael Freedman, 1986 winner of the Fields medal, the highest
prize in mathematics, and a quantum computing specialist at
Microsoft Station Q at the University of California, Santa
Barbara. "I admire their approach, which is to be suspicious
of anything -- electrons, photons, Maxwell's equations -- that
everyone else accepts as fundamental."
Herbertsmithite -- a model of a two dimensional universe?
Other theories that describe light and electrons also exist,
of course; Wen and Levin realize that the burden of proof is
on them. It may not be far off. Their theory also describes
possible new states with emergent light-like and electron-like
excitations in some condensed matter systems, and Young Lee's
group at MIT might have found such a system. Motivated by the
theoretical developments that predict spin liquid states with
fractionalized quasiparticles, Young Lee decided to look for
such materials. Trawling through geology journals, his team
spotted a candidate -- a dark green crystal that geologists
stumbled across in the mountains of Chile in 1972. "The
geologists named it after a mineralogist they really admired,
Herbert Smith, labeled it and put it to one side," says Young
Lee. "They didn't realize the potential herbertsmithite would
have for physicists years later." Herbertsmithite (pictured)
is unusual because its electrons are arranged around triangles
in a two dimensional Kagome lattice. Normally, electrons
prefer to have their spins to be in the opposite direction to
that of their immediate neighbors, but in a triangle this is
impossible -- there will always be neighboring electrons
spinning in the same direction. Such kind of frustration makes
spins in herbertsmithite not to know where to point to and to
form a random fluctuating state -- a spin liquid. Although
herbertsmithite exists in nature, the mineral contains
impurities that prevent us to study the spin state, says Young
Lee. So Daniel Nocera's group at MIT made a pure sample in the
lab for Young Lee's group to study it. "It was painstaking,"
says Young Lee. "It took us a full year to prepare it and
another year to analyze it." The team measured the degree of
spin magnetization in the material, in response to an applied
magnetic field. If herbertsmithite behaves like ordinary
matter, they argue, then below about 26C the spins of its
electrons should stop fluctuating and point to certain fixed
directions -- a condition called magnetic order. But the team
found no such transition, even down to just a fraction of
degree above absolute zero. They measured other properties,
too, such as heat capacity. In conventional solids, the
relationship between their temperature and their ability to
store heat changes below a certain temperature, because the
structure of the material changes. The team found no sign of
such a transition in herbertsmithite, suggesting that, unlike
other types of matter, its lowest energy state has no
discernible order. "We could have created something in the lab
that nobody has seen before," says Young Lee. The unordered
state -- the spin liquid state -- that they discovered is
likely to be an example of string-net liquids, since all
theoretically known spin liquids are string-net liquids. In
particular, Ying Ran, Michael Hermele, Patrick Lee, and
Xiao-Gang Wen from MIT proposed that the spins in
herbertsmithite may form a particular spin liquid that
contains light-like excitations described by Maxwell's
equations and electron-like excitations described by Dirac
equation. In other words, herbertsmithite might realize a
particular string-net liquid, which mimic a two dimensional
universe with light and electrons. The team plans further
tests to probe the spins of electrons, looking for long-range
entanglement by firing neutrons at the crystal and observing
how they scatter. "We want to see the dynamics of the spin,"
says Young Lee. "If we tweak one [spin], we can see how the
others are affected." This intrigues Paul Fendley, a
theoretical physicist at the University of Virginia,
Charlottesville. "It's reasonable to hope that we are seeing
something exotic here," he says. "People are getting very
excited about this." Even if herbertsmithite is not a new
state of matter, we shouldn't be surprised if one is found
soon, as many teams are hunting for them, says Freedman. He
says people wrongly assume that particle accelerators are the
only places where big discoveries about matter can be made.
"Accelerators are just recreating conditions after the big
bang and repeating experiments that are old hat for the
universe," he says. "But in labs people are creating
[conditions] that are colder than anywhere that has ever
existed in the universe. We are bound to stumble on something
the universe has never seen before."
----------------------------------------------------------------
Silicon for a quantum age
Herbertsmithite could be the new silicon the building block
for quantum computers. In theory, quantum computers are far
superior to classical computers. In practice, they are
difficult to construct because quantum bits, or qubits, are
extremely fragile. Even a slight knock can destroy stored
information. In the late 1980s, mathematician Michael
Freedman, then at Harvard University, and Alexei Kitaev, then
at the Landau Institute for Theoretical Physics in Russia,
independently came up with a radical solution to this problem.
Instead of storing qubits in properties of particles, such as
an electron's spin, they suggested that qubits could be
encoded into properties shared by the whole material, and so
would be harder to disrupt (New Scientist, 24 January 2004, p
30). "The trouble is the physical materials we know about,
like the chair you're sitting on, don't actually have these
exotic properties," says Freedman. Physicists told Freedman
that the material he needed simply didn't exist, but Young
Lee's group at MIT might just prove them wrong. The material
would be a string-net liquid where ends of strings behaving
like quasi-particles with fractional charge or spin.
Physicists could manipulate quasi-particles (ie ends of
strings) with electric or magnetic fields, braiding them
around each other, encoding information in the number of times
the strings twist and knot, says Freedman. A disturbance might
knock the whole braid, but it won't change the number of
twists protecting the information. "The hardware itself would
correct any errors," says Miguel Angel Martin-Delgado of
Complutense University in Madrid, Spain. If herbertsmithite is
described by the particular spin liquid proposed by Ran etal,
then it is not suitable to do quantum computing since the
excitations are gapless. If, instead, herbertsmithite is
described by a gapped spin liquid (or string-net liquid), then
it might be suitable for quantum computing. -- Xiao-Gang Wen
References
Visible links
1.
http://www.newscientist.com/article.ns?id=mg19325954.200&feedId=fundamentals_rss20
http://free.naplesplus.us/links/click.php?url=http%3A%2F%2Fwww.newscientist.com%2Farticle.ns%3Fid%3Dmg19325954.200%26feedId%3Dfundamentals_rss20
2.
http://en.wikipedia.org/wiki/Kagome_lattice
http://free.naplesplus.us/links/click.php?url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FKagome_lattice
3.
http://www.newscientist.com/article.ns?id=mg19325954.200&feedId=fundamentals_rss20
4.
http://www.mindat.org/min-26600.html
