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Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter."1 MoreReceived 17 June 2017DOI:https://doi.org/10.1103/RevModPhys.89.040502© 2017 Nobel Foundation, Published by The American Physical Society*The 2016 Nobel Prize for Physics was shared by David J. Thouless, F. Duncan M. Haldane, and John Michael Kosterlitz. These papers are the text of the address given in conjunction with the award.Physics Subject Headings (PhySH)Research AreasTopological defectsTopological phase transitionTopological phases of matterGeneral PhysicsInterdisciplinary Physics
F. D. M. Haldane (Mon,) studied this question.