## Event Date:

## Event Date Details:

Refreshments served at 3:40pm.

## Event Location:

- Broida 1640

- Physics Colloquium

The 2016 Nobel Prize in Physics was awarded to D. J. Thouless, F. D. M. Haldane, and J. M. Kosterlitz for "theoretical discoveries of topological phase transitions and topological phases of matter". The major work of Haldane, for which the Prize was awarded, was the remarkable prediction that the ground-state property of the quantum Heisenberg antiferromagnetic chain is qualitatively different depending on whether the spin quantum number is an integer or a half-odd-integer; there is a non-vanishing excitation gap only in integer-spin chains. Most of us learned from textbooks, reviews, and lectures that the original prediction was based on the topological term of the effective field theory of the quantum spin chain, the O(3) non-linear sigma model. However, recollections by Haldane himself, and the discovery of the "lost paper" revealed that the original discovery of the "Haldane gap" was based on a rather different argument, which was closely related to Berezinskii-Kosterlitz-Thouless transition, another work for which the 2016 Prize was awarded. In this talk, I will review the history of "Haldane conjecture" which has had a fascinating twist perhaps because it was too revolutionary at the time, and its influence over the development of contemporary condensed matter physics.