Choreographed entangle dances: topological states of quantum matter

For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at zero temperature, even symmetric disordered liquids can have features, which give rise to topological phases of quantum matter. Some of the topological phases are highly entangled (i.e. have topological order), while others are weakly entangled (i.e. have SPT order). In this article, we will briefly introduce those new zero-temperature states of matter and their amazing emergent properties. We will also discuss their significance in unifying some most basic concepts in nature.