Related papers: A random matrix model with localization and ergodi…
We study the transition from a many-body localized phase to an ergodic phase in spin chain with correlated random magnetic fields. Using multiple statistical measures like gap statistics and extremal entanglement spectrum distributions, we…
Using exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one…
The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria of parameter dependent motion in the system and consider measures such as level…
Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features governing the critical transition…
The delocalized non-ergodic phase existing in some random $N \times N$ matrix models is analyzed via the Wigner-Weisskopf approximation for the dynamics from an initial site $j_0$. The main output of this approach is the inverse…
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization…
The Anderson localization transition in quantum graphs has garnered significant recent attention due to its relevance to many-body localization studies. Typically, graphs are constructed using top-down methods. Here, we explore a bottom-up…
We introduce new diagnostics of the transition between the ergodic and many-body localization phases, which are based on complexity measures defined via the probability distribution function of the Lanczos coefficients of the…
Anderson localization on random regular graphs (RRG) serves as a toy-model of many-body localization (MBL). We explore the transition for ergodicity to localization on RRG with large connectivity $m$. In the analytical part, we focus on the…
Utilizing the framework of free probability, we analyze the spectral and operator statistics of the Rosenzweig-Porter random matrix ensembles, which exhibit a rich phase structure encompassing ergodic, fractal, and localized regimes.…
The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to…
The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified…
We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
The scaling theory of Anderson localization is based on a global conductance $g_L$ that remains a random variable of order O(1) at criticality. One realization of such a conductance is the Landauer transmission for many transverse channels.…
The ensemble of $L \times L$ power-law random banded matrices, where the random hopping $H_{i,j}$ decays as a power-law $(b/| i-j |)^a$, is known to present an Anderson localization transition at $a=1$, where one-particle eigenfunctions are…
Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same…
The Rosenzweig-Porter model has seen a resurgence in interest as it exhibits a non-ergodic extended phase between the ergodic extended metallic phase and the localized phase. Such a phase is relevant to many physical models from the…
We study the spectral properties of the adjacency matrix in the giant connected component of Erd\"os-R\'enyi random graphs, with average connectivity $p$ and randomly distributed hopping amplitudes. By solving the self-consistent cavity…
We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival…