  We consider a model of restricted dimers coupled to two-dimensional causal
dynamical triangulations (CDT), where the dimer configurations are restricted
in the sense that they do not include dimers in regions of high curvature. It
is shown how the model can be solved analytically using bijections with
decorated trees. At a negative critical value for the dimer fugacity the model
undergoes a phase transition at which the critical exponent associated to the
geometry changes. This represents the first account of an analytical study of a
matter model with two-dimensional interactions coupled to CDT.
