相关论文: Localization and fractality in disordered Russian …
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…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that…
The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the…
Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase.…
We formulate a real-space renormalization group (RG) approach for efficient numerical analysis of the low-temperature hopping dynamics in energy-disordered lattices. The approach explicitly relies on the time-scale separation of the…
We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models…
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…
We revisit the problem of an elastic line (e.g. a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond…
Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase and ergodic transition have a status of a mathematical theorem. Yet, this phase in GRP model is oversimplified: the spectrum of…
Renormalization Group (RG) theory provides the theoretical framework to define Effective Theories (ETs), i.e. systematic low-resolution approximations of arbitrary microscopic models. Markov State Models (MSMs) are shown to be rigorous ETs…
We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the…
We investigate the 1D Anderson-Hubbard model at half filling with box-disorder. The ground state phase diagram is obtained by means of real-space dynamical mean-field theory (R-DMFT) and the density matrix renormalization group (DMRG). We…
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 investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of…
We propose a tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex…
We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random…
We present exact analytical results revealing the existence of a countable infinity of unusual single particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond shaped loops as the…
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By…
We consider the relation between the \Omega -deformed N=2 SQCD with the single deformation parameter and integrable models of the BCS-like superconductivity. It is argued that the vortex string worldsheet theory is related to the Russian…