Abstract
By exactly diagonalizing the Hubbard model for ten electrons on ten sites in a one-Dimensional (1D) ring, we extend the study of Jafari (2008) to more than two electrons on two sites. We equally show the sparsity patterns of the Hamiltonian matrices for four- and eight-site problems and obtain the ground state energy eigenvalues for ten electrons on ten-sites. The technique we employ will be a good guide to a beginner/programmer.
Highlights
The Hubbard model (Hubbard, 1963) has been the basic formalism for treating the electron-electron correlations in interacting many-body systems ever since the advent of high-TC superconductors
Exact Diagonalization (ED) technique is unique among the various numerical techniques available because it is unbiased, simple and straightforward
The sparsity pattern of the Hamiltonian matrix for our ten electrons on ten sites problem showed that only 2128532 entries or 0.0062% are non-zeroes
Summary
The Hubbard model (Hubbard, 1963) has been the basic formalism for treating the electron-electron correlations in interacting many-body systems ever since the advent of high-TC superconductors. By exactly diagonalizing the Hubbard model, using some intrinsic routines in MATLAB® (R2010a), we present the ground state energy for N electrons on N The sparsity pattern of the Hamiltonian matrix is presented.
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