The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz for their theoretical discoveries of topological phase transition and topological phases of matter. This article introduces their research experiences and describes the awarded achievements, as well as the scientific background and later development, from the aspects of topology and topological phase transitions, topology in quantum Hall effect, one dimensional antiferrom agnet and symmetry-protected topological states.

2016 Nobel Prize in Physics  /  phase transition  /  topological phase transition  /  topological phases