A. Mildenberger

Exact relations between multifractal exponents at the anderson transition

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices

Multifractality of wave functions at the quantum Hall transition revisited

q<1/2

Multifractality at the quantum Hall transition: beyond the parabolic paradigm.

to those with

Dimensionality dependence of the wave-function statistics at the Anderson transition

q>1/2

Surface Criticality and Multifractality at Localization Transitions

. The second relation connects the wave function multifractality to that of Wigner delay times in a system with a lead attached.

Wavefunction statistics and multifractality at the spin quantum Hall transition

We investigate numerically the statistics of wave function amplitudes ψ(r) at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of ‖ψ‖ 2 is log-normal, so that the multifractal spectrum f( α) is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.

Multifractality at the spin quantum Hall transition

We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Deltaq characterizing anomalous scaling of wave function moments |psi|2q at the quantum Hall transition. The result reads Deltaq=2q(1-q)[b0+b1(q-1/2)2+cdots, three dots, centered], with b0=0.1291+/-0.0002 and b1=0.0029+/-0.0003. The central finding is that the spectrum is not exactly parabolic: b1 not equal0. This rules out a class of theories of the Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

Density of quasiparticle states for a two-dimensional disordered system : Metallic, insulating, and critical behavior in the class-D thermal quantum hall effect

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPRs)

Wave function statistics at the symplectic two-dimensional Anderson transition: Bulk properties

{P}_{q}

Boundary multifractality in critical one-dimensional systems with long-range hopping

is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.