The physics of Anderson transitions between localized and metallic phases in disordered
systems is reviewed. The term “Anderson transition” is understood in a broad sense …

Applications of neural networks to condensed matter physics are becoming popular and
beginning to be well accepted. Obtaining and representing the ground and excited state …

The non-Hermitian skin effect, anomalous localization of an extensive number of eigenstates
induced by nonreciprocal dissipation, plays a pivotal role in non-Hermitian topology and …

The fractional Laplacian operator−(− Δ) α∕ 2 appears in a wide class of physical systems,
including Lévy flights and stochastic interfaces. In this paper, we provide a discretized …

We study the effect of quasiperiodic Aubry-André disorder on the energy spectrum and
eigenstates of a one-dimensional all-band-flat (ABF) diamond chain. The ABF diamond …

We study spectral and wave-function statistics for many-body localization transition in
systems with long-range interactions decaying as 1/r α with an exponent α satisfying d≤ α≤ …

Eigenstates of local many-body interacting systems that are far from spectral edges are
thought to be ergodic and close to being random states. This is consistent with the …

Multifractal dimensions allow for characterizing the localization properties of states in
complex quantum systems. For ergodic states the finite-size versions of fractal dimensions …

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 …

arxiv:cond-mat/0609580v1 [cond-mat.mes-hall] 22 Sep 2006 Page 1 arxiv:cond-mat/0609580v1
[cond-mat.mes-hall] 22 Sep 2006 submitted to acta physica slovaca 1– 123 NUMERICAL …