In order to explore a possibility of superfluidity in confined strongly-correlated fermion systems, e.g., nano-scale cuprate High-Tc superconductors and atomic Fermi gases loaded on optical lattice, we implement an exact diagonalization code for their mathematical model, i.e., a trapped Hubbard model on the Earth Simulator. We compare two diagonalization algorithms, the traditional Lanczos meth...

Application of Eisenstat-SSOR Preconditioner to Realistic Stress Analysis Problem by Parallel Cache-Cache Computing Kuniyoshi Abe1, Seiji Fujino2 1Faculty of Economics and Information, Gifu Shotoku University, Japan; 2Professor Emeritus, Kyushu University, Japan Communication avoiding Neumann expansion preconditioner for LOBPCG method: Convergence property of exact diagonalization method for Hu...

In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson’s Numerical Renormalization Group (NRG) and White’s Density Matrix ...

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 present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm includes a generalization of the look-up method introduced in Ref. [1] and enables massively parallel execution matrix-vector linear operations required by Lanczos Arnoldi algorithms. show that suitable Fock basis organization is crucial optimize inter-processors communication distribu...

Exact diagonalization study of the two-dimensional t − J−Holstein model (Received today) We study by exact diagonalization the two-dimensional t − J−Holstein model near quarter filling by retaining only few phonon modes in momentum space. This truncation allows us to incorporate the full dynamics of the retained phonon modes. The behavior of the kinetic energy, the charge structure factor and o...

Some technical aspects of Cluster Perturbation Theory (CPT) are presented. CPT is an approximation scheme for calculating the oneparticle Green function of the Hubbard model of interacting electrons on a lattice. It proceeds by (i) dividing the lattice into identical clusters and calculating the Green function by exact diagonalization on a given cluster (ii) extending this Green function to the...

We have used an exact diagonalization technique to study the stability of the t − J-Holstein and Hubbard-Holstein models under the influence of the electron-phonon interaction. Previous results have been obtained using frozen-phonon technique or introducing only a few dynamical phonon modes due to the large Hilbert space. To check these results we have done exact diagonalization in a small clus...