http://phys.columbia.edu/~nhc/tdl80th/presentations/wen.pdf
concise frank summary of deep questions in physics -- Xiao-Gang Wen On Tue, Oct 22, 2013 at 7:23 PM, Rich Murray <[email protected]> wrote: > http://dao.mit.edu/~wen/pub/qorder.html > > Theory of quantum orders and string-net condensation > Back to Home page . > A unification of light and electrons through string-net condensation in > spin models (pdf) > Michael A. Levin and Xiao-Gang Wen > cond-mat/0407140 > String-net condensation provides a way to unify light and electrons. > > String-net condensation: A physical mechanism for topological phases (pdf) > Michael Levin and Xiao-Gang Wen > Phys. Rev. B71, 045110 (2005). cond-mat/0404617 > Pointed out that all the gauge theories and doubled Chern-Simons theories > can be realized in lattice spin models through different string-net > condensations. > Found a mechanism to make the ends of condensed string to have Fermi, > fractionali, or non-Abelian statistics > Found the mathematical foundation of topological order and string-net > condensation -- Tensor Category Theory. > Used tensor category theory to classify all T and P symmetric topological > orders. > > Quantum order from string-net condensations and origin of light and > massless fermions (pdf) > Xiao-Gang Wen > Phys. Rev. D68, 024501 (2003). hep-th/0302201 > Quantum ordered states that produce and protect massless gauge bosons and > massless fermions are string-net condensed states. > Different string-net condensations are not characterized by symmetries, > but by projective symmetry group (PSG). PSG describes the symmetry in the > hopping Hamiltonian for the ends of condensed strings. > PSG protects masslessness of Dirac fermions. PSG leads to an emerging > chiral symmetry. > Constructed an local boson model on cubic lattice that has emerging QED > and QCD. > > Fermions, strings, and gauge fields in lattice spin models (pdf) > Michael Levin and Xiao-Gang Wen > Phys. Rev. B67, 245316 (2003). cond-mat/0302460 > Pointed out that fermions can emerge in local bosonic models as ends of > open strings. > The string picture for fermions works in any dimensions, which is more > general than flux-binding picture in 2D. > Pointed out that emerging fermions always carry gauge charges. > > Quantum Orders and Spin Liquids in Cs2CuCl4 (pdf) > Yi Zhou and Xiao-Gang Wen > cond-mat/0210662 > Classified the symmetric spin liquids on triangular lattice. > Identified 63 Z2 spin liquids, 30 U(1) spin liquids and 2 SU(2) spin > liquids. > Suggested that the U1C0n1 spin liquid or one of its relatives may describe > the spin liquid state in Cs2CuCl4 > > Artificial light and quantum order in systems of screened dipoles (pdf) > Xiao-Gang Wen > Phys. Rev. B68, 115413 (2003). cond-mat/0210040 > Constructed realistic screened dipole systems in 2D and 3D that contain > artificial photon as their low energy collective excitations. > Find that a U(1) gauge theory is actually a dynamical theory of nets of > closed strings. > According to the string-net picture, a gapless gauge boson is a > fluctuation of large closed strings and charge is the end of open strings. > > Quantum Orders in an exact soluble model (pdf) > Xiao-Gang Wen > Phys. Rev. Lett. 90, 016803 (2003). quant-ph/0205004 > Constructed an exact soluble spin-1/2 model on square lattice > The ground states of the model can have different quantum orders at > different couplings. > The model has topological degenerate ground states and non-chiral gapless > edge excitations described by Majorana fermion. > > Gapless Fermions and Quantum Order (pdf) > X.-G. Wen and A. Zee > Phys. Rev. B66, 235110 (2002). cond-mat/0202166 > Showed that gapless fermions can originate from and be protected by > certain quantum orders, even for pure bosonic systems which originally > contain no fermions. > > Origin of Light (pdf) > Origin of Gauge Bosons from Strong Quantum Correlations > Xiao-Gang Wen > Phys. Rev. Lett. 88 11602 (2002) hep-th/0109120 > Proposed that light is originated from certain quantum orders. > Constructed a spin model (which can sit on your palm) that reproduces a > complete 1+3D QED at low energies. > At the editor's request, the published version got a new and longer title. > > Quantum Order: a Quantum Entanglement of Many Particles (pdf) > (or a Quantum Waltz of Many) > Xiao-Gang Wen > Physics Letters A 300, 175 (2002). cond-mat/0110397 > A gentler introduction of quantum orders. > Pointed out that > Quantum Order = Pattern of quantum entanglement > Gauge Bosons = Fluctuations of quantum entanglement. > The paper was rejected by PRL (referee's comments) ;-( > > Quantum Orders and Symmetric Spin Liquids > The original version (pdf 1.3Mb) > The published version (pdf 1.2Mb) > Xiao-Gang Wen > Phys. Rev. B65, 165113 (2002). cond-mat/0107071 > Introduced a concept -- quantum order. > Introduced a mathematical object Projective Symmetry Group (PSG) to > (partially) characterize the quantum orders. > Used PSG to classify the quantum orders in over 100 different symmetric > spin liquids. > Proposed to use neutron scattering to measure quantum orders in high Tc > superconductors. > Showed that quantum order can produce and protect gapless excitations > (including light) without breaking any symmetries. > (The symmetric spin liquids all have the same translation, rotation, > parity and time reversal symmetries. Thus they cannot be characterized by > the Landau's theory and the symmetry breaking principle. Symmetric spin > liquids can only be distinguished by their different quantum orders.) > At editor and referee's request, I have to remove the appendix (the main > calculations) from the published version. (;-/ > The complete work can be found at cond-mat/0107071. > > > > > On Tue, Oct 22, 2013 at 7:07 PM, Rich Murray <[email protected]> wrote: > >> http://dao.mit.edu/~wen/NSart-wen.html >> >> 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 >> >> >> On Tue, Oct 22, 2013 at 4:29 PM, Alan Fletcher <[email protected]> wrote: >> >>> > From: "Axil Axil" <[email protected]> >>> > Sent: Tuesday, October 22, 2013 2:42:34 PM >>> >>> > 8 million bucks to move north. That signings bonus is almost as >>> lucrative a >>> > pitching relieve in the big leagues. He must be good to rate that kind >>> of >>> > money. >>> >>> That's not $8M for Wen -- it's the capital to establish a chair, the >>> proceeds of which will pay a particular holder of the chair. >>> >>> >> >
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