Laboratoire de Physique Théorique
Toulouse - UMR 5152

Anderson transitions (ATs) between metals and insulators or between topologically distinct insulators, share common features with conventional second-order phase transitions, such as the critical point of the Ising model for a magnet. However, ATs also exhibit many unusual features including the multifractal scaling of the critical wave functions. Conventional critical points possess conformal invariance which constrain their properties to the extent that they can be obtained exactly in two dimensions and to very high precision in three dimensions. Until recently, researchers assumed that Anderson transitions also possess conformal invariance and can be described by conformal field theories (CFTs). I will review recent progress in understanding the relation between conformal invariance and mutifractal wave functions. The emerging picture puts serious doubt on the ability of CFTs to properly describe multifractality at ATs in both two and three dimensions.