相关论文: Non-ergodic extended states in $\beta$-ensemble
The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus…
We consider disordered tight-binding models which Green's functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D_{1} that…
Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of…
We uncover a new non-ergodic phase, distinct from the many-body localized (MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The dynamics of this emergent phase, which has no single-particle analog and exists only…
We study the spectral rigidity of the non-Hermitian analog of the Anderson model suggested by Tzortzakakis, Makris and Economou (TME). This is a $L\times L \times L$ tightly bound cubic lattice, where both real and imaginary parts of…
Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis,…
The asymptotic (non)equivalence of canonical and microcanonical ensembles, describing systems with soft and hard constraints respectively, is a central concept in statistical physics. Traditionally, the breakdown of ensemble equivalence…
The mobility edge is extracted from a non-perturbative analysis of F. Wegner's real matrix ensemble (RME), $N$-orbital model of electrons with broken time-reversal invariance moving in random potential. The replicon fluctuations around the…
In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many…
We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are…
Recent studies on disorder-induced many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. However, the non-Hermitian disorder-free MBL still needs to be clarified. We consider a one-dimensional…
We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both…
Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq \beta \leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the…
The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a site's southerly and westerly nearest neighbors have spin $1$, it may reset its own spin by tossing a…
The presence of disorder can severely impede wave transport, resulting in the famous Anderson localization. Previous theoretical studies found that Anderson transition can exist in one-dimensional (1D) non-Hermitian disordered rings with…
Some interacting disordered many-body systems are unable to thermalize when the quenched disorder becomes larger than a threshold value. Although several properties of nonzero energy density eigenstates (in the middle of the many-body…
The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$.…
Our study connects the physics of disordered integer-dimensional systems and regular self-similar objects by studying spectral properties of fractal agglomerates with tunable dimension. The latter is controlled by parameter $\alpha$ of the…
Anderson localization on tree-like graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the…
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…