Topological Phase Transitions & Topological Matter
F. Duncan M. Haldane & J. Michael Kosterlitz (David J. Thouless was also awarded but unable to lecture)
About This Prize
The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter.” Their pioneering work revealed that topology — a branch of mathematics describing properties preserved under continuous deformations — plays a fundamental role in understanding exotic phases of matter. Kosterlitz and Thouless explained phase transitions in two-dimensional systems using topological defects, while Haldane discovered that topological concepts apply to chains of small magnets and predicted a quantum Hall effect without an external magnetic field.
F. Duncan M. Haldane
“Topological Quantum Matter”
J. Michael Kosterlitz
“Topological Defects and Phase Transitions”
Key Concepts
- • Kosterlitz-Thouless (KT) Phase Transition: A topological phase transition in 2D systems driven by the binding and unbinding of vortex-antivortex pairs
- • Topological Invariants: Integer quantities that protect quantum states from smooth perturbations, explaining robustness of certain phases
- • Haldane Model: A theoretical model demonstrating a quantum Hall effect without an external magnetic field, using a honeycomb lattice
- • Topological Insulators and Beyond: Materials that are insulators in the bulk but conduct on their surfaces via topologically protected edge states