  Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation
of Quantum Gravity assuming the existence of a global time foliation. In our
earlier study we analyzed the effect of including $d$ copies of a massless
scalar field in the two-dimensional CDT model with imaginary time. For $d > 1$
we observed the formation of a "blob", somewhat similar to that observed in
four-dimensional CDT without matter. In the two-dimensional case the "blob" has
a Hausdorff dimension $D_H=3$. In this paper we study the spectral dimension
$D_S$ of the two-dimensional CDT-universe, both for $d = 0$ (pure gravity) and
$d = 4$. We show that in both cases the spectral dimension is consistent with
$D_S = 2$.
