Rudolf A. Roemer

Multifractal finite-size scaling and universality at the Anderson transition

We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L3=1203 and involving nearly 106 independent wave functions have yielded unprecedented precision for the critical disorder Wc=16.530(16.524,16.536) and the critical exponent ν=1.590(1.579,1.602). We find that the multifractal exponents Δq exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [ Phys. Rev. Lett. 105 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.

Excitonic Aharonov-Bohm effect in a two-dimensional quantum ring

We study theoretically the optical properties of an exciton in a two-dimensional ring threaded by a magnetic flux. We model the quantum ring by a confining potential that can be continuously tuned from strictly one-dimensional to truly two-dimensional with finite radius-to-width ratio. We present an analytic solution of the problem when the electron-hole interaction is short ranged. The oscillatory dependence of the oscillator strength as a function of the magnetic flux is attributed to the Aharonov-Bohm effect. The amplitude of the oscillations changes upon increasing the width of the quantum ring. We find that the Aharonov-Bohm oscillations of the ground state of the exciton decrease with increasing the width, but, remarkably, the amplitude remains finite down to radius-to-width ratios less than unity. We attribute this resilience of the excitonic oscillations to the nonsimple connectedness of our chosen confinement potential with its centrifugal core at the origin.

Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging

We study the multifractal analysis (MFA) of electronic wavefunctions at the localisation-delocalisation transition in the 3D Anderson model for very large system sizes up to

Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices

240^3

Controlled engineering of extended states in disordered systems

. The singularity spectrum

Dimensionless ratios: characteristics of quantum liquids and their phase transitions

f(\alpha)

Self-assembling tensor networks and holography in disordered spin chains

is numerically obtained using the \textsl{ensemble average} of the scaling law for the generalized inverse participation ratios

Digital electron diffraction – seeing the whole picture

P_q

Spin-polarized electric current in silicene nanoribbons induced by atomic adsorption

, employing box-size and system-size scaling. The validity of a recently reported symmetry law [Phys. Rev. Lett. 97, 046803 (2006)] for the multifractal spectrum is carefully analysed at the metal-insulator transition (MIT). The results are compared to those obtained using different approaches, in particular the typical average of the scaling law. System-size scaling with ensemble average appears as the most adequate method to carry out the numerical MFA. Some conjectures about the true shape of

Data for Manifestation of many-body interactions in the integer quantum Hall effect regime

f(\alpha)