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Related papers: Localization of weakly disordered flat band states

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We consider a general class of $n\times n$ random band matrices with bandwidth $W$. When $W^2\ll n$, we prove that with high probability the eigenvectors of such matrices are localized and decay exponentially at the sharp scale $W^2$.…

Probability · Mathematics 2025-08-29 Reuben Drogin

The realization of robust quantum storage devices relies on the ability to generate long-lived, spatially localized quantum states. In this work, we introduce a method for the targeted creation of compact excitations in flat-band lattices.…

Optics · Physics 2026-02-12 Carlo Danieli , Jie Liu , Rudolf A. Römer , Rodrigo A. Vicencio

We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that…

Localization of coherent propagating waves has been extensively studied over the years, primarily in homogeneous random media. However, significantly less attention has been given to wave localization in inhomogeneous systems, where the…

Disordered Systems and Neural Networks · Physics 2026-01-27 Alejandro Ramírez-Yañez , Thomas Gorin , Rodrigo A. Vicencio , Víctor A. Gopar

By employing Random Matrix Theory (RMT) and first-principle calculations, we investigated the behavior of Anderson localization in 1D, 2D and 3D systems characterized by a varying disorder. In particular, we considered random binary layer…

Optics · Physics 2012-08-23 D. Molinari , A. Fratalocchi

Flat bands result in a divergent density of states and high sensitivity to interactions in physical systems. While such bands are well known in systems under magnetic fields, their realization and behavior in zero-field settings remain…

Strongly Correlated Electrons · Physics 2025-08-05 Chen-Xin Jiang , Zi-Xiang Hu , Bo Yang

We study large $N\times N$ power-law random band matrices $H=(H_{ij})$ with centered complex Gaussian entries, where the variances satisfy a power-law decay $\mathbb{E}|H_{ij}|^2\propto (|i-j|/W+1)^{-1-\alpha}$, for some exponent…

Probability · Mathematics 2026-04-15 Jiaqi Fan , Fan Yang , Jun Yin

We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators…

Mesoscale and Nanoscale Physics · Physics 2026-03-05 Carlo Danieli , Sergej Flach

In flat-band systems with quenched kinetic energy, most of the conventional length scales related to the band dispersion become ineffectual. Although a few geometric length scales, such as the quantum metric length, can still be defined,…

Mesoscale and Nanoscale Physics · Physics 2025-12-01 Seokju Lee , Seung Hun Lee , Bohm-Jung Yang

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…

Optics · Physics 2020-08-12 Gabriel Caceres-Aravena , Luis E F Foa , Rodrigo A Vicencio

We present a method for realizing various zero-energy localized states on disorder-free hypercube graphs. Previous works have already indicated that disorder is not essential for observing localization phenomena in noninteracting systems,…

Disordered Systems and Neural Networks · Physics 2025-07-02 Ievgen I. Arkhipov , Fabrizio Minganti , Franco Nori

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states…

Strongly Correlated Electrons · Physics 2015-05-28 Rajyavardhan Ray , Avinash Singh

In moir\'e superlattices, the band flatness governs the degree of wave localization, which is central to harnessing emergent phenomena and designing functional meta-devices. While research has focused on the magic conditions such as magic…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

Mathematical Physics · Physics 2012-05-08 Victor Chulaevsky

In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a…

Pattern Formation and Solitons · Physics 2009-11-13 Rodrigo A. Vicencio And Sergej Flach

Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly…

Quantum Physics · Physics 2026-05-15 Anish Acharya , Luca Giuggioli , Shamik Gupta

Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures…

Strongly Correlated Electrons · Physics 2013-05-29 Dmitry Green , Luiz Santos , Claudio Chamon

We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more…

Disordered Systems and Neural Networks · Physics 2020-02-20 Attila Szabó , Ulrich Schneider

Flat bands have become a pillar of modern condensed matter physics and photonics owing to the vanishing group velocity and diverging density of states. Here, we present a paradigmatic scheme to construct arbitrary flat bands on demand by…

Optics · Physics 2025-11-27 Moru Song , Jingyu Hu , Lina Shi , YongliangZhang , Kai Chang

In disordered systems, the amplitudes of the localized states will decrease exponentially away from their centers and the localization lengths are characterizing such decreasing. In this article, we find a model in which each eigenstate is…

Disordered Systems and Neural Networks · Physics 2023-09-04 Ye Xiong