The exact vacuum polarization 4-tensor in the presence of a static magnetic field is calculated by a method due to Svetozarova and Tsytovich. The Hermitian part of the tensor is explicitly renormalized by Shabad’s diagonalization with respect to tensor indices and the anti-Hermitian part of the tensor is found to be finite and gauge invariant. An alternative method for calculating the vacuum po...

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground-state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact-ground-state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharm...

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343-356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained...

We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in the initial diagonalization. The method is part of a new approach to computational quantum physics which combines both diagonalization and Monte Carlo techni...

We theoretically study the excitation spectrum of confined macroscopic optical lattices in the Mott-insulating limit. For large systems, a fast numerical method is proposed to calculate the ground state filling and excitation energies. We introduce many-particle on-site energies capturing multi-band effects and discuss tunnelling on a perturbative level using an effectively restricted Hilbert s...

The self-consistent cranking method is tested by comparing the cranking calculations in the interacting boson model with the exact results obtained from the SU~3! and O~6! dynamical symmetries and from numerical diagonalization. The method is used to study the spin dependence of shape variables in the sd and sdg boson models. When realistic sets of parameters are used, both models lead to simil...

In recent years there has been a renewed interest in the study of strongly correlated electron materials. These materials exhibit interesting phenomena like the correlation induced metal insulator transition [1–3]. A very promising method capable of providing a theoretical description, perhaps, is the limit of large spatial dimensions [4], which defines a dynamical mean field theory for the pro...

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...

The Kohn-Sham equation in first-principles density functional theory (DFT) calculations is a nonlinear eigenvalue problem. Solving the nonlinear eigenproblem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshevfiltered subspace iteration (CheFSI) ...

2 The cluster approach 4 2.1 Tiling the lattice into small clusters . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Cluster perturbation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Green’s function and exact diagonalization . . . . . . . . . . . . . . . . . . . . 5 2.4 Freedom in the CPT construction . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 The Ritz...