  We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by $ H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]$. We study by exact numerical diagonalization of $H$ the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as $L^{-z}$ where the gap exponent $z$
is approximately $2.55\pm 0.15$. This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.
