Rational Jacobi matrices and certain quantum mechanical problems
M. C. Boscá, J. S. Dehesa · Journal of Physics A Mathematical and General · 1984
In several branches of physics the Hamiltonian of a many-body system can be reduced to a rational Jacobi matrix (i.e. a Jacobi matrix whose elements are rational functions of the suffix) by means of a method of the Lanczos type. Here it is shown that one can calculate in a simple analytical way the asymptotic eigenvalue density of all these matrices by means of its moments without solving the corresponding eigenvalue problem. The method is applied to a large class of quantum mechanical models of Hamiltonians.