  The Husimi distribution is proposed for a phase space analysis of quantum
phase transitions in the two-dimensional $U(3)$ vibron model for $N$-size
molecules. We show that the inverse participation ratio and Wehrl's entropy of
the Husimi distribution give sharp signatures of the quantum (shape) phase
transition from linear to bent. Numerical results are complemented with a
variational approach using parity-symmetry-adapted $U(3)$ coherent states,
which reach the minimum Wehrl entropy $\frac{N(3+2N)}{(N+1)(N+2)}$, in the
rigidly linear phase, according to a generalized Wehrl-Lieb conjecture. We also
propose a characterization of the vibron-model quantum phase transition by
means of the zeros of the Husimi distribution.
