  We study the localization in the Hilbert space of a modified
Tomonaga-Luttinger model. For the standard version of this model, the states
are found to be extended in the basis of Slater determinants, representing the
eigenstates of the non-interacting system. The linear dispersion which leads to
the fact that these eigenstates are extended in the modified model is replaced
by one with random level spacings modeling the complicated one-particle spectra
of realistic models. The localization properties of the eigenstates are
studied. The interactions are simplified and an effective one-dimensional Lloyd
model is obtained. The effects of many-body energy correlations are studied
numerically. The eigenstates of the system are found to be localized in Fock
space for any strength of the interactions, but the localization is not
exponential.
