  We study a chaotic particle-conserving kinetically constrained model, with a
single parameter which allows us to break reflection symmetry. Through
extensive numerical simulations we find that the domain wall state shows a
variety of dynamical behaviors from localization all the way to ballistic
transport, depending on the value of the reflection breaking parameter.
Surprisingly, such anomalous behavior is not mirrored in infinite-temperature
dynamics, which appear to scale diffusively, in line with expectations for
generic interacting models. However, studying the particle density gradient, we
show that the lack of reflection symmetry affects infinite-temperature
dynamics, resulting in an asymmetric dynamical structure factor. This is in
disagreement with normal diffusion and suggests that the model may also exhibit
anomalous dynamics at infinite temperature in the thermodynamic limit. Finally,
we observe low-entangled eigenstates in the spectrum of the model, a telltale
sign of quantum many body scars.
