Centro de Excelencia Severo Ochoa
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The Nobel Prize in Physics this year has fallen in three theoretical physicists, David Thouless, Duncan Haldane and Michael Kosterlitz.The Royal Swedish Academy of Sciences has granted this prestigious award for its "theoretical discoveries of topological phase transitions andtopological phases of matter".
These findings date from the 70s and 80s of last century, and sowed the seeds of a new paradigm for understanding the nature that can be summed up in the term "topological matter." Topology is the branch of mathematics that describes the properties of geometric objects that do not change by smooth deformations such as stretch or shrink. The application of topological concepts in physics is what has awarded the Nobel Prize. In the 70s, Kosterlitz and Thouless showed that superfluidity and superconductivity in thin films were possible thanks to the existence of topological defects called vortices. A decade later, Thouless and colleagues explained mathematically the topological nature of the electrical conductivity in the quantum Hall effect. In the 80s, Haldane predicted that spin chains with integer spin 1, 2, .. had a spectral and very differenttopological properties from those of half-integer spin chains ½, 3/2, ... All these discoveries were the advance of the insulators, metals and topological superconductors.This talk will present an introduction to these topics