A New Type of Symmetry Discovered in Nature

by Carsten Andrew Lutken (University of Oslo, Norway)

Wednesday 29 Jan 2020, 13:00 → 14:00 Europe/Madrid

IFAE Seminar Room (IFAE)

Although the QHE is one of the cornerstones of modern metrology, four decades and several Nobel prizes after its discovery it continues to strain our understanding of quantum mechanics.
A comprehensive review of experiments probing the quantum Hall effect (QHE) provides substantial support for a conjecture that the morass of Hall data conceals a new type of symmetry of great utility and beauty, which is called modular.

The mathematical roots of these infinite discrete symmetries date back to Archimedes and  Apollonius. Twenty-three centuries later they are central to many recent developments in string theory and mathematics, including the proof of Fermat’s last theorem. Also familiar from some of M.C.  Escher ́s finest prints of nested fractal structures, like his famous “Angels and Demons” motif, this type of symmetry has not previously been seen in Nature.

By leveraging this symmetry an effective field theory capable of modeling all universal aspects of the QHE is developed to a point where it can be compared with scaling data. In order to exhibit the modular symmetry seen in experiments, the target space of this emergent sigma model is a torus.

Toroidal geometry permits a quantum equivalence known as mirror symmetry, which together with other results from string theory enables the construction of the topological part of the partition function. This gives us access to the non-perturbative structure of the theory, including a phase diagram that automatically unifies the fractional and integer Hall effect.

While the location of quantum critical points and critical exponents derived from this model agree with numerical experiments at the per mille level, a reliable comparison with real experimental data awaits better finite-size scaling experiments.