We investigate the sensitivity of the problem of Non-Orthogonal (matrix) Joint Diagonalization (NOJD). First, we consider the uniqueness conditions for the problem of Exact Joint Diagonalization (EJD), which is closely related to the issue of uniqueness in tensor decompositions. As a by-product, we derive the well-known identifiability conditions for Independent Component Analysis (ICA), based ...

Modern ab initio and multiscale methods enable the simulation of vibrational properties of very large molecules. Within the harmonic approximation, the traditional generation of the spectra based on the force field diagonalization can become inefficient due to the excessive demands on computer time and memory. The present study proposes to avoid completely the matrix diagonalization with a dire...

A software library is presented for the polynomial expansion method (PEM) of the density of states (DOS) introduced in Ref [1, 2]. The library provides all necessary functions for the use of the PEM and its truncated version (TPEM) in a model independent way. The PEM/TPEM replaces the exact diagonalization of the one electron sector in models for fermions coupled to classical fields. The comput...

We study the Anderson model of localization with anisotropic hopping in three dimensions for weakly coupled chains and weakly coupled planes. The eigenstates of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes up to 48 3 , show multifractal behavior at the metal-insulator transition even for strong anisotropy. The critical disorder strength W c determined from the sy...

The calculation of twoand four-particle observables is addressed within the framework of the truncated polynomial expansion method (TPEM). The TPEM replaces the exact diagonalization of the one-electron sector in models for fermions coupled to classical fields such as those used in manganites and diluted magnetic semiconductors. The computational cost of the algorithm is O(N) – with N the numbe...

In this paper, the electronic eigenstates and energy spectra of single and two-interacting electrons confined in a concentric double quantum rings with a perpendicular magnetic field in the presence of         on-center donor and acceptor impurities are calculated using the exact diagonalization method. For a single electron case, the binding energy of on-center donor and acceptor impurities ar...

We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe ansatz local-density approximation BALDA to the density functional theory formulation of the Hubbard model. This is capable of describing both Luttinger liquid and Mott-insulator correlations. The BALDA ...

We present the results of exact diagonalization calculations of the isolated and isothermal on-site static susceptibilities in the anisotropic extended Heisenberg model on a linear chain with periodic boundary conditions. Based on the ergodicity considerations we conclude that the isothermal susceptibility will diverge as T → 0 both in finite clusters and in the bulk system in two non-ergodic r...

The magnetization process of the S = 1 and 1/2 kagomé Heisenberg antiferromagnet is studied by means of the numerical exact diagonalization method. It is found that the magnetization curve at zero temperature has a plateau at 1/3 of the full magnetization. In the presence of √ 3 × √ 3 lattice distortion, this plateau is enhanced and eventually the ferrimagnetic state is realized. There also app...

We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding preci...