Related papers: Localization-delocalization transition for a rando…
We consider random matrices of the form $H = W + \lambda V$, $\lambda\in\mathbb{R}^+$, where $W$ is a real symmetric or complex Hermitian Wigner matrix of size $N$ and $V$ is a real bounded diagonal random matrix of size $N$ with i.i.d.\…
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($\mathcal{PT}$) symmetry. The localization transition induced by…
We investigate delocalization phenomena for eigenvectors of real random matrices that are invariant by orthogonal transformations. A specific phenomenon with these ensembles is that an eigenvector is typically more localized when its…
We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. \dots,…
Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-Andr\'{e}-Harper model with irrational modulations in the…
We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is considered as a phase detection parameter for delocalized-localized phase transition. By employing one-dimensional models that undergo delocalized-localized phase…
We examine quantum percolation on a square lattice with random dilution up to $q=38%$ and energy $0.001 \le E \le 1.6$ (measured in units of the hopping matrix element), using numerical calculations of the transmission coefficient at a much…
We study the ultrametric random matrix ensemble, whose independent entries have variances decaying exponentially in the metric induced by the tree topology on $\mathbb{N}$, and map out the entire localization regime in terms of…
In this text, we consider an N by N random matrix X such that all but o(N) rows of X have W non identically zero entries, the other rows having lass than $W$ entries (such as, for example, standard or cyclic band matrices). We always…
Let $\mathcal A$ be the adjacency matrix of the Erd\H{o}s-R\'{e}nyi directed graph $\mathscr G(N,p)$. We denote the eigenvalues of $\mathcal A$ by $\lambda_1^{\cal A},...,\lambda^{\cal A}_N$, and $|\lambda_1^{\cal A}|=\max_i|\lambda_i^{\cal…
This work provide a thorough study of L\'evy or heavy-tailed random matrices (LM). By analysing the self-consistent equation on the probability distribution of the diagonal elements of the resolvent we establish the equation determining the…
We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-Andr\'{e} potential and a hopping amplitude which is varied periodically in time. Our analysis shows the…
Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…
In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88,…
Single-electron capacitance spectroscopy precisely measures the energies required to add individual electrons to a quantum dot. The spatial extent of electronic wavefunctions is probed by investigating the dependence of these energies on…