Theory of quantum orders and stringnet condensation
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A unification of light and electrons through
stringnet condensation in spin models
(pdf)
Michael A. Levin and XiaoGang Wen
condmat/0407140

Stringnet condensation provides a way to unify light and electrons.

Stringnet condensation: A physical mechanism for topological phases
(pdf)
Michael Levin and XiaoGang Wen
Phys. Rev. B71, 045110 (2005).
condmat/0404617

Pointed out that all the gauge theories and doubled ChernSimons theories
can be realized in lattice spin models through different stringnet
condensations.

Found a mechanism to make the ends of condensed string to have Fermi,
fractionali, or nonAbelian statistics

Found the mathematical foundation of topological order and stringnet
condensation  Tensor Category Theory.

Used tensor category theory to classify all T and P symmetric topological
orders.

Quantum order from stringnet condensations
and origin of light and massless fermions
(pdf)
XiaoGang Wen
Phys. Rev. D68, 024501 (2003).
hepth/0302201

Quantum ordered states that produce and protect massless gauge
bosons and massless fermions are stringnet condensed states.

Different stringnet 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 XiaoGang Wen
Phys. Rev. B67, 245316 (2003).
condmat/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 fluxbinding picture in 2D.

Pointed out that emerging fermions always carry gauge charges.

Quantum Orders and Spin Liquids in Cs2CuCl4
(pdf)
Yi Zhou and XiaoGang Wen
condmat/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)
XiaoGang Wen
Phys. Rev. B68, 115413 (2003).
condmat/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 stringnet 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)
XiaoGang Wen
Phys. Rev. Lett. 90, 016803 (2003).
quantph/0205004

Constructed an exact soluble spin1/2 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 nonchiral gapless edge
excitations described by Majorana fermion.

Gapless Fermions and Quantum Order
(pdf)
X.G. Wen and A. Zee
Phys. Rev. B66, 235110 (2002).
condmat/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
XiaoGang Wen
Phys. Rev. Lett. 88 11602 (2002)
hepth/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)
XiaoGang Wen
Physics Letters A 300, 175 (2002).
condmat/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)
XiaoGang Wen
Phys. Rev. B65, 165113 (2002).
condmat/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
condmat/0107071.
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