For Hans,

Topological order: from long-range entangled quantum matter to an
unification of light and electrons

Xiao-Gang Wen
(Submitted on 4 Oct 2012)
In primary school, we were told that there are four states of matter:
solid, liquid, gas, and plasma. In college, we learned that there are
much more then four states of matter. For example, the phenomenon of
magnetization reveals the existence of ferromagnetic phases and the
phenomenon of zero-viscosity reveals the existence of superfluid
phases. There many more phases in our rich world, and it is amazing
that those phases can be understood systematically by the symmetry
breaking theory of Landau. In this paper, we will review the progress
in last 20 -- 30 years, during which we discovered that there are many
new phases that cannot be described Landau symmetry breaking theory.
We discuss new "topological" phenomena, such as topological
degeneracy, that reveal the existence of those new phases --
topologically ordered phases. Just like zero-viscosity define the
superfluid order, the new "topological" phenomena define the
topological order at macroscopic level. More recently, we find that,
at microscopical level, topological order is due to long-range quantum
entanglements, just like fermion superfluid is due to fermion-pair
condensation. Long-range quantum entanglements lead to many amazing
emergent phenomena, such as fractional quantum numbers,
fractional/non-Abelian statistics, and protected gapless boundary
excitations. We find that long-range quantum entanglements (or
topological order) provide a unified origin of light and electrons:
light waves are fluctuations of long-range entanglements, and fermions
are defects of long-range entanglements. Long-range quantum
entanglements (and the related topological order) represent a new
chapter and a future direction of condensed matter physics, or even
physics in general.
Comments: A gentle review of topological order. 41 pages 22 figures\

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