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A mysterious green crystal may be challenging our most basic ideas about matter and even space-time itself

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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."

-- Xiao-Gang Wen

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