Related papers: Decorrelation estimates for a 1D tight binding mod…
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…
An entanglement spectrum encodes statistics beyond the entanglement entropy, of which several have been studied in the context of many-body localization. We numerically study the extreme value statistics of entanglement spectra of many-body…
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter $N\times N$ random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase.…
In this paper, we investigate the open tight-binding model with $N$ sites coupled to two reservoirs on its edges with the nonequilibrium Green function method to understand effects of open boundaries. As a result, we obtain an analytical…
In this paper, the asymptotic behavior of abstract strongly coupled hyperbolic equations with one infinite memory term is investigated, one specific case of which is the model for describing the dynamical behaviour of magnetic effected…
Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an…
Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…
A derivation method is given which leads to a series of tight Bell inequalities for experiments involving N parties, with binary observables, and three possible local settings. The approach can be generalized to more settings. Ramifications…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
While entanglement plays an important role in characterizing quantum many-body systems, it is hardly possible to directly access many-body entanglement in real experiments. In this paper, we study how bipartite entanglement of many-body…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
We derive a simple sufficient criterion for the locality of correlations obtained from given measurements on a Gaussian quantum state. The criterion is based on the construction of a local-hidden-variable model which works by passing part…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an…
We study the discrete constrained saddle dynamics and their momentum variants for locating saddle points on manifolds. Under the assumption of exact unstable eigenvectors, we establish a local linear convergence of the discrete constrained…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…