# Quantum percolation transition in 3d: density of states, finite size scaling, and multifractality

## László Ujfalusi

### (Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics)

Time: Tue May 20 13:00:00 2014

Location: Building 1, Room 114, Auditorium

Since the seminal work of Anderson we know that disorder plays an important role of conductivity properties of a system. For the investigation of structural disorder, percolation is one of the most important and widely used models. With increasing disorder, extended states of a perfect crystal turn into localized states through a second order phase transition called Anderson-transition. At criticality the system is scale-free, leading to multifractal eigenstates of the Hamiltonian. We used this spectacular property of the wave functions to identify the mobility edge, the energy-dependent critical point of the quantum percolation model. The critical exponent of the localization length was found to be 𝜇=1.627±0.055, in very good agreement with the one for the Anderson-model, confirming that these models belong to the same universality class. The multifractal exponents were also determined, and we found certain deviations from our expectations. The very special density of states of the model will also be presented along with its special chiral molecular states at the band center.