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In 1972 J. Michael Kosterlitz and David J. Thouless identified a completely new type of phase transition in two-dimensional systems where topological defects play a crucial role.

Their theory applied to certain kinds of magnets and to superconducting and superfluid films, and has also been very important for understanding the quantum theory of one-dimensional systems at very low temperatures.

In the early 1980s David J. Thouless and F. Duncan M. Haldane developed theoretical methods to describe phases of matter that cannot be identified by their pattern of symmetry breaking.

In a 1982 paper, David Thouless and his collaborators Mahito Kohmoto, Peter Nightingale, and Marcel den Nijs, explained the very precise quantization of the Hall conductance in two- dimensional electron gases using topological concepts. In 1983 Duncan Haldane derived a theory for spin chains that incorporated effects of topology in a crucial way. Based on this he predicted that chains with integer and half-integer spins should be qualitatively different, and this totally unexpected effect was later confirmed by experiments.

This prize is a tribute to the innovative use of elegant mathematical concepts toward

simplification and better understanding of strongly interacting systems of many quantum particles.

A full account can be found at the nobel site prize: Scientific background on the Nobel Prize in Physics 2016

where three of the references are to the book by the Physics Department chair, Assa Auerbach, and to papers by Yosi Avron and Ari Turner.

Note that:

David Thouless was one of the LITP's earliest distinguished lecturers in 1997, speaking on ''Topological Quantum Numbers''

F. Duncan M. Haldane participated serval LITP conferences , the last conference was in last June “Interacting Electrons and Quantum Magnetism” ( see his talk at youtube)