New Scientist published an 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

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 Störmer 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