1210.1281 (Xiao-Gang Wen)

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

Xiao-Gang Wen

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.

View original: http://arxiv.org/abs/1210.1281