  We present an exact analytical solution for quantum strong long-range models
in the canonical ensemble by extending the classical solution proposed in
[Campa et al., J. Phys. A 36, 6897 (2003)]. Specifically, we utilize the
equivalence between generalized Dicke models and interacting quantum models as
a generalization of the Hubbard-Stratonovich transformation. To demonstrate our
method, we apply it to the Ising chain in transverse field and discuss its
potential application to other models, such as the Fermi-Hubbard model,
combined short and long-range models and models with antiferromagnetic
interactions. Our findings indicate that the critical behaviour of a model is
independent of the range of interactions, within the strong long-range regime,
and the dimensionality of the model. Moreover, we show that the order parameter
expression is equivalent to that provided by mean-field theory, thus confirming
the exactness of the latter. Finally, we examine the algebraic decay of
correlations and characterize its dependence on the range of interactions in
the full phase diagram.
