Quantum correlated heat engine in XY chain with Dzyaloshinskii-Moriya interactions

In this paper, we consider a heat engines composed of two interactional qubits with spin-orbit interaction (Dzyaloshinskii-Moriya (DM)) subject to an external magnetic field, so that each qubit is coupled with cold or hot source. One intention of this work is to investigate the following question: is it possible the effects of DM lead to improve basic thermodynamic quantities in this heat engine are coupled to local environments that are not necessarily at equilibrium? Moreover, we study whether or not quantum correlations can be helpful in the performance of quantum work engines. For this end, we investigate the effects of the temperature and the interaction rate of each qubit with its surrounding environment on quantum correlations such as quantum coherence and quantum discord and quantum entanglements, as well as the generated work. Finally we compare three quantum correlations (entanglement, discord, and coherence) with thermodynamic parameters and show that the output work is positive for what values of the magnetic field so that this cycle can be considered as a thermal machine.