  Conventional diagonalization methods to calculate nuclear energy levels in
the framework of the configuration-interaction (CI) shell model approach are
prohibited in very large model spaces. The shell model Monte Carlo (SMMC) is a
powerful technique for calculating thermal and ground-state observables of
nuclei in very large model spaces, but it is challenging to extract nuclear
spectra in this approach. We present a novel method to extract low-lying energy
levels for given values of a set of good quantum numbers such as spin and
parity. The method is based on imaginary-time one-body density correlation
matrices that satisfy asymptotically a generalized eigenvalue problem. We
validate the method in a light nucleus that allows comparison with exact
diagonalization results of the CI shell model Hamiltonian. The method is
applicable to other finite-size quantum many-body systems that can be described
within a CI shell model approach.
