Chaotic wave functions and exponential convergence of low-lying energy eigenvalues

We suggest that low-lying eigenvalues of realistic many-body Hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated by the diagonalization of truncated matrices with the exponential extrapola tion of the results. We show numerical data confirming this conjecture. We argue that the exponential convergence may be a generic feature of complex systems where the wave functions are localized in an appropriate basis.