  We study how a quantum heat engine performs across the critical value of an
external parameter, pertaining to the quantum phase transition. Considering a
two-ion system subjected to a magnetic field, we show that the system performs
in a quantum Otto cycle above a critical value of the magnetic field, while
below such critical point, it does not operate in a heat cycle at all.
Moreover, at the critical point, its interaction with an ancillary ion
deteriorates the performance of the system as a heat engine. We further show
that a strong interaction between the constituent ions of an ion-based system
is crucial for it to work in a heat-work cycle, while the coupling to the
ancillary system must be minimized.
