Critical level statistics and anomalously localized states at the Anderson transition

H. Obuse; K. Yakubo

doi:10.1103/physrevb.71.035102

Home/Archive/arXiv

arXiv · cond-mat/0405429

Critical level statistics and anomalously localized states at the Anderson transition

H. Obuse·K. Yakubo

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.

Explore related subjects

cond-mat.dis-nn cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

H. Obuse, K. Yakubo. 2005-01-07. Critical level statistics and anomalously localized states at the Anderson transition. https://doi.org/10.1103/physrevb.71.035102

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Tunable periodic cascade of delocalization transitions in non-Hermitian IAAF model

Cascade of delocalization transitions provides a route to multi-step control of delocalization, yet achieving a programmable periodic cascade remains a challenge. Here, we demonstrate a tunable periodic cascade of delocalization transitions in a non-Hermitian interpolating Aubry-André-Fibonacci (IAAF) model by introducing an imaginary phase shift into the quasiperiodic potential. Such a periodic cascade of delocalization transitions arises from the competition between kinetic-energy-facilitated delocalization and gain-loss-regulated localization. In numerical static localization characterizations, successive regular stripe patterns for localized and extended states emerge in phase diagrams. We also derive an analytical expression for the cascade period and find that it relies solely on the imaginary phase shift. This provides a direct way of continuously tuning the cascade period via a single control parameter. Complementary static and dynamical diagnostics consistently confirm this periodic cascade of delocalization transitions in the non-Hermitian IAAF system. Our findings identify a novel class of delocalization transitions with tunable cascading periods, opening a route toward experimentally programmable control of delocalization.

cond-mat.dis-nn↗

arXiv2026

Microscopic Mechanism and Control of Reentrant Localization

Increasing quasiperiodic modulation can restore extended states after localization, raising the question of how the same modulation drives both localization and recovery. We identify a microscopic mechanism in quasiperiodic dimer chains by resolving scattering between Fourier channels. Specifically, scattering into neighboring channels and back shifts the spectral edge relative to a localization boundary determined by a neutral auxiliary resonance. Their successive crossings drive the same spectral packet with fixed integrated-density-of-states (IDS) labels into localization and back into an extended regime. This recovery persists across finite parameter ranges in both gap-opening families, including relative-phase detuning. Furthermore, an exact sublattice mapping enables compensated control of the recovery window and predicts recovery thresholds for individual IDS labels.

cond-mat.dis-nn↗

arXiv2026

Dynamical mean-field theory for associative memory with block-correlated patterns

In associative memories storing correlated patterns, retrieval of individual memories can compete with symmetric mixed states. A dynamical description is needed to determine how the initial state selects between these outcomes. We extend the generating-functional dynamical mean-field theory (DMFT) for independent patterns to independent blocks of correlated binary patterns of fixed finite size. The resulting effective single-neuron process has a self-consistent cross-talk noise covariance and self-feedback coefficients that depend on the block-covariance eigenvalues. For hierarchically correlated patterns with nonmonotonic transfer, increasing the loading can permit retrieval from an imperfect initial state before further loading prevents it. DMFT reproduces the retrieval trajectories and basin geometry found in direct simulations. Near the lower boundary of this re-entrant region, direct networks reveal stationary saddles separating coexisting mixed and target-retrieval states. Parameter sensitivities of DMFT trajectories predict nearby shifts of this boundary. At the tested upper boundary, retrieval remains accessible from initial states with larger target overlap, indicating a change in basin access. Under fixed-point convergence assumptions, the theory recovers the equations of generalized self-consistent signal-to-noise analysis.

cond-mat.dis-nn↗