A non-integrable representation of the Heisenberg Algebra

Question

Let $\mathfrak h$ be the Heisenberg algebra in dimension 1, generated by vectors $P$, $Q$ and $I$ satisfying $[P,Q] = I$, $[P,I] = [Q,I] = 0$. A representation of $\mathfrak h$ on a Hilbert space $X$ is a lie algebra homomorphism from $\mathfrak h$ to the set of linear operators on $X$ (with the commutator bracket). Such a representation is called integrable if there is a corresponding representation $\rho$ of the Heisenberg group $H$ such that $P = \frac{d}{dt}|_{t=0} \rho(\exp(tP))$ and $Q = \frac{d}{dt}|_{t=0} \rho(\exp(tQ))$, where $U$ and $V$ are the one-parameter unitary groups generated by the generators of the Heisenberg group. I am looking for an example of a representation of $\mathfrak h$ which is not integrable. Does anyone have one?