  We use a simple real-space renormalization group approach to investigate the
critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum
spin chain possessing a line of criticality along which critical exponents vary
continuously. This approach, which is based on exploiting the on-site symmetry
of the model, has been shown to be surprisingly accurate for predicting some
aspects of the critical behavior of the Ising model. Our investigation explores
this approach in more generality, in a model where the critical behavior has a
richer structure but which reduces to the simpler Ising case at a special
point. We demonstrate that the correlation length critical exponent as
predicted from this real-space renormalization group approach is in broad
agreement with the corresponding results from conformal field theory along the
line of criticality. Near the Ising special point, the error in the estimated
critical exponent from this simple method is comparable to that of
numerically-intensive simulations based on much more sophisticated methods,
although the accuracy decreases away from the decoupled Ising model point.
