Exact diagonalization techniques

Abstract

In this chapter we show how to calculate a few eigenstates of the full Hamiltonian matrix of an interacting quantum system. Naturally, this implies that the Hilbert space of the problem has to be truncated, either by considering finite systems or by imposing suitable cut-offs, or both. All of the presented methods are iterative, i.e., the Hamiltonian matrix is applied repeatedly to a set of vectors from the Hilbert space. In addition, most quantum many-particle problems lead to a sparse matrix representation of the Hamiltonian, where only a very small fraction of the matrix elements is non-zero. © Springer-Verlag Berlin Heidelberg 2008.