  In this article we demonstrate that dynamical quantum phase transitions occur
for an exemplary higher order topological insulator, the
Benalcazar-Bernevig-Hughes model, following quenches across a topological phase
boundary. A dynamical bulk boundary correspondence is also seen both in the
eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The
latter is found from a finite size scaling analysis for which the relative
simplicity of the model is crucial. Contrary to the usual two dimensional case
the dynamical quantum phase transitions in this model show up as cusps in the
return rate, as for a one dimensional model, rather than as cusps in its
derivative as would be typical for a two dimensional model. We explain the
origin of this behaviour.
