相关论文: Random Matrices with Correlated Elements: A Model …

{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous…

We study the level-statistics of a disordered system undergoing the Anderson type metal-insulator transition. The disordered Hamiltonian is a sparse random matrix in the site representation and the statistics is obtained by taking an…

Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized…

The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…

The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of disordered interacting one-dimensional many-particle system is studied. The average of the first entanglement…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…

We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles…

I address here the question of the mutual interplay of strong correlations and disorder in the system. I consider random version of the Hubbard model. Diagonal randomness is introduced {\it via} random on-site energies and treated by the…

Higher order parametric level correlations in disordered systems with broken time-reversal symmetry are studied by mapping the problem onto a model of coupled Hermitian random matrices. Closed analytical expression is derived for parametric…

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…

We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated…

We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders behaves in a way similar to that of the single parametric Brownian ensembles. The latter appear during aPoisson…

We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…

We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…

We propose a working strategy to describe the eigenvalue statistics of random spin systems along the whole phase diagram with thermal to many-body localization (MBL) transition. Our strategy relies on two random matrix (RM) models with…