Update: One of my readers was able to attend the first two talks of the Kavli Symposium, by Duncan Haldane and Michael Kosterlitz, two of this year's Nobel laureates. Here are his comments. If anyone has observations about the remaining talks in the symposium, please feel free to email me or post in the comments below.
I basically ran from the Buckley Prize talk by Alexei Kitaev down the big hall where Duncan Haldane was preparing to talk. When I got there it was packed full but I managed to squeeze into a seat in the middle section. I sighted my postdoc near the back of the first section; he later told me he’d arrived 35 minutes early to get that seat.I felt Haldane’s talk was remarkably clear and simple given the rarified nature of the physics behind it. He pointed out that condensed matter physics really changed starting in the 1980’s, and conceptually now is much different than the conventional picture presented in books like Ashcroft and Mermin’s Solid State Physics that many of us learned from as students. One prevailing idea leading up to that time was that changes in the ground state must always be related to changes in symmetry. Haldane’s paper on antiferromagnetic Heisenberg spin chains showed that the ground state properties of the chains were drastically different depending on whether the spin at each site is integer (S=1,2,3,…) or half-integer (S=1/2, 3/2, 5/2 …) , despite the fact that the Hamiltonian has the same spherical symmetry for any value of S. This we now understand on the basis of the topological classifications of the systems. Many of these topological classifications were later systematically worked out by Xiao-Gang Wen who shared this year’s Buckley prize with Alexei Kitaev. Haldane flashed a link to his original manuscript on spin chains which he has posted on arXiv.org as https://arxiv.org/abs/1612.00076 , and which he noted was “rejected by many journals”. He was also amused or bemused or maybe both by the fact that people referred to his ideas as “Haldane’s conjecture” rather than recognizing that he’d solved the problem. He noted that once one understands that the topological classification determines many of the important properties it is obvious that simplified “toy models” can give deep insight into the underlying physics of all systems in the same class. In this regard he singled out the AKLT model, which revealed how finite chains of spin S=1 have effective S=1/2 degrees of freedom associated with each end. These are entangled with each other no matter how long the finite chain – a remarkable demonstration of quantum entanglement over a long distance. This also is a simple example of the special nature of surface states or excitations in topological systems.Kosterlitz began by pointing out that the Nobel prize was effectively awarded for work on two distinct aspects of topology in condensed matter, and both of these involved David Thouless which led to his being awarded one-half of the prize, with the other half shared by Kosterlitz and Haldane. He then relayed a bit about his own story: he started as a high energy physicist, and apparently did not get offered the position he wanted at CERN so he ended up at Birmingham, which turned out to be remarkably fortuitous. There he teamed with Thouless and gradually switched his interests to condensed matter physics. They wanted to understand data suggesting that quasi-two-dimensional films of liquid helium seemed to show a phase transition despite the expectation that this should not be possible. He then gave a very professorial exposition of the Kosterlitz-Thouless (K-T) transition, starting with the physics of vortices, and how their mutual interactions involve a potential that depends on the logarithm of the distance. The results point to a non-zero temperature above which the free energy favors free vortices and below which vortex-anti vortex pairs are bound. He then pointed out how this is relevant to a wide variety of two dimensional systems, including xy magnets, and also the melting of two-dimensional crystals in which two K-T transitions occur corresponding respectively to the unbinding of dislocations and disclinations.
I greatly enjoyed both of these talks, especially since I have experimentally researched both spin chains and two-dimensional melting at different times in my career.