Anomalously localised states at the Anderson transition

Abstract

Non-multifractal critical wave functions at the Anderson transition are numerically investigated for the SU(2) model belonging to the two-dimensional symplectic class. These states can be regarded as anomalously localised states (ALS) at criticality. Giving a quantitative definition of ALS, it has been revealed that the probability to find ALS increases with the system size and remains at a finite value even in the thermodynamic limit. The most probable, namely typical, critical states have the multifractal nature, while its probability measure is zero. In order to understand how ALS affect critical properties in infinite systems, we studied the distribution of the correlation dimension D2 and the nearest-neighbour level spacing distribution P(s) by paying attention to ALS. Results show that the influence of ALS to these distribution functions is limited. This is because the spatial distribution of amplitudes in tail regions of ALS exhibits multifractality as in the case of typical critical wave functions.