  We introduce new families of pure quantum states that are constructed on top
of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this
by constructing unitaries as the exponential of operators quadratic in Cartan
subalgebra elements and by applying these unitaries to regular group-theoretic
coherent states. This enables us to generate entanglement not found in the
coherent states themselves, while retaining many of their desirable properties.
Most importantly, we explain how the expectation values of physical observables
can be evaluated efficiently. Examples include generalized spin-coherent states
and generalized Gaussian states, but our construction can be applied to any Lie
group represented on the Hilbert space of a quantum system. We comment on their
applicability as variational families in condensed matter physics and quantum
information.
