Haldane on the second quantum revolution

This week I attended a great public lecture by Duncan Haldane: "Quantum Mechanics After One Hundred Years, and the 'Second Quantum Revolution' Today"

Starting from the discovery of quantum mechanics, he explained how the concept of quantum entanglement is fueling today's second quantum revolution and its connection to his Nobel Prize-winning work.

Haldane remarked that his work on quantum spin chains was controversial. He had theorists accosting him at conferences arguing he was wrong. These kinds of disputes among theorists are best settled by experiment. Undoubtedly, Haldane would not have received his Nobel Prize if his predictions had not been validated by experiments. How can you motivate some experimental group to be interested in your theory? If it generates controversy!

Similarly, experiments often are the drive for fresh theoretical advances. For example, the experimental discovery of the quantum Hall and fractional quantum Hall effects came before the theoretical predictions or understanding. 

A good example of this is a second important work by Haldane also cited in his prize: quantum Hall effects in absence of Landau levels. This now-seminal work went largely unnoticed for a decade, because the model based on a two-dimensional honeycomb lattice seemed unfeasible to realize in an experiment. Later, the unanticipated work experimental isolation of graphene drove theorists to this fresh area. Haldane's early theory work was recognised as the foundation for the discovery of time reversal-symmetric topological insulators and the whole "zoo" of topological materials that followed.

Haldane also emphasized the importance of luck in making ground-breaking discoveries. von Klitzing was not the first person to attempt quantum Hall measurements, but previous attempts had used a different experimental setup: varying current with a fixed magnetic field. Imperfections in the current source led to fluctuations in the measured resistivity, which seemed to be consistent with previous approximate theoretical calculations based on perturbation theory. von Klitzing's approach of measuring resistivity as a function of magnetic field strength, with current kept fixed, led to unexpectedly precise quantization which needed new theory to explain. 

Haldane's take-home message was thus: anyone can win a Nobel Prize, but you need luck and the perseverance to defend your work if it is challenged.

An earlier iteration of this talk is available here. A more detailed write-up is available here.