Many-body quantum thermal machines in a Lieb-kagome Hubbard model

Quantum many-body systems serve as a suitable working medium for realizing quantum thermal machines (QTMs) by offering distinct advantages such as cooperative many-body effects, and performance boost at the quantum critical points. However, the bulk of the existing literature exploring the criticality of many-body systems in the context of QTMs involves models sans the electronic interactions, which are non-trivial to deal with and require sophisticated numerical techniques. Here we adopt the prototypical Hubbard model in two dimensions (2D) in the framework of the line graph Lieb-kagome lattice for the working medium of a multi-functional QTM. We resort to a non-perturbative, static path approximated (SPA) Monte Carlo technique to deal with the repulsive Hubbard model. We observe that in a Stirling cycle, in both the interacting and non-interacting limits, the heat engine function dominates and its performance gets better when the strain is induced from the kagome to the Lieb limit, while for the reverse the refrigeration action is preferred. Further, we show that the QTM performs better when the difference between the temperatures of the two baths is lower and the QTM reaches the Carnot limit in this regime. Further, we extensively study the performance of the QTM in the repulsive Hubbard interacting regime where the magnetic orders come into the picture. We explore the performance of the QTM along the quantum critical points and in the large interaction limit.