Theory of quantum orders and string-net condensation
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  1. 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.
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  3. 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.
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  5. 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.
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  7. 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.
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  9. 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
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  11. 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.
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  13. 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.
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  15. 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.
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  17. 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.
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  19. 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) ;-(
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  21. 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.
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