  Algebraic methods for solving time dependent Hamiltonians are used to
investigate the performance of quantum thermal machines. We investigate the
thermodynamic properties of an engine formed by two coupled q-bits, performing
an Otto cycle. The thermal interaction occurs with two baths at different
temperatures, while work is associated with the interaction with an arbitrary
time-dependent magnetic field that varies in intensity and direction. For the
coupling, we consider the 1-d isotropic Heisenberg model, which allows us to
describe the system by means of the irreducible representation of the
$\mathfrak{su}(2)$ Lie algebra within the triplet subspace. We inspect
different settings of the temperatures and frequencies of the cycle and
investigate the corresponding operation regimes of the engine. Finally, we
numerically investigate the engine efficiency under a time varying Rabi
frequency, interpolating the abrupt and adiabatic limits.
