  The enhancement of quantum heat engines (QHEs) efficiency is of great
interest for fundamental studies and quantum technology developments, where
collective many-body effects play an important role. In this work we analyze
the efficiency of two QHEs where the working substance exhibits second order
quantum phase transitions (QPT). One of these engines is defined by the working
substance corresponding to the anisotropic Lipkin-Meshkov-Glick (LMG) model and
the other to the full Dicke model. We consider that, working at thermal
equilibrium, the heat engines realize a thermodynamic Stirling cycle type. For
both QHEs, a remarkable enhancement of efficiency is obtained when during the
cycle the working substances undergo a QPT, where eventually the efficiency
reaches the Carnot bound. We also analyze the effect of the degree of
anisotropy in the interaction term of the LMG model and the unbalance between
rotating and counter-rotating terms in the full Dicke model. It is observed a
better efficiency increase when the interaction term in the LMG model is more
anisotropic, and in the full Dicke model, when the rotating and
counter-rotating interaction terms are equally balanced. We discuss an
equivalence between our Stirling cycle and the Carnot cycle at some particular
values of the model parameters, where maximum efficiencies are attained. It is
also analyzed how the ground state degeneracy in the QPT is associated to such
maximum efficiency. Finally, these behaviors are related to the symmetries of
the models that break at the phase transition.
