  Properties of the yrast states of a system of $N$ bosons confined to a
one-dimensional ring and interacting via contact forces is examined both
variationally and by numerical diagonalizations. The latter allow for obtaining
numerical correlated many-body wave functions explicitly. The study of
correlation functions involving different yrast states indicates that a quantum
phase transition previously detected in the properties of the ground state in
the case of attractive two-body interactions is an yrast phenomenon involving
the onset of `deformation', in the sense given to this term by Bohr and
Mottelson in connection with the description of nuclear spectra, including
enhanced transition operators and emergence of a shared intrinsic correlation
structure. In this case the moment of inertia of the deformed state is
essentially the rigid moment of inertia, `intrinsic' states being essentially
degenerate.
