Highly Entangled Quantum Matter

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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 are so many phases in our rich world, and it is amazing that those phases can be understood systematically by the symmetry breaking theory of Landau. But our world is even richer and more amazing. In this proposal, we are going to study a totally new class of quantum matter that is beyond Landau symmetry breaking theory. We will study new "topological" phenomena 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 the macroscopic level. Recently, we found that, at the 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 charges, fractional/non-Abelian statistics, and perfect conducting edge channels. We find that long-range quantum entanglements (or topological order) can even provide a unified origin of light and electrons: light waves are fluctuations of long-range entanglements, and electrons 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.