Theory seminar: Modular Symmetry in Nature

Carsten Lütken, UiO

The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the predicted location of quantum critical points is in accurate agreement with experiments.

The symmetry severely constrains the effective low energy physics of 10¹⁰ charges in two dirty dimensions. A toroidal σ­‐model gives a critical exponent that is in close agreement with numerical simulations. A double scaling law uncovered in the data suggests that the wave­‐function may be multi‐fractal.

The modular analysis can be extended to “relativistic” group IV materials like graphene, silicene, germanene and stanene, and where reliable data are available there appears to be agreement.

C.A. Lütken, Introduction to the role of modular symmetries in graphene and other 2-­‐dimensional materials, Contemp. Phys. (2014), http://dx.doi.org/10.1080/00107514.2014.949445

C.A. Lütken, G.G. Ross, Quantum critical Hall exponents, Phys. Lett. A 378 (2014) 262–265, http://dx.doi.org/10.1016/j.physleta.2013.11.001