Entropy and specific heat features of a four spin system at its energy level crossings

Abstract

A previous study showed that the efficiency of a quantum heat engine utilizing the Lipkin-Meshkov-Glick (LMG) spin system can reach the Carnot limit at low temperatures when the external field reaches the energy level cross points of the ground states. These points occur when different energy levels become degenerate. To delve more into the quantum behavior at the crossing points, this work considered the thermodynamic characteristics of an LMG model consisting of four spins. Using the eigenenergies for the N = 4 spin system with anisotropy, the entropy, and specific heat were numerically obtained in the canonical ensemble and studied as a function of its energy level crossings. It is found that lower values of energy level crossings correspond to more stable entropies and higher specific heat values of the system. These features make the LMG spin system suitable as a working substance in heat engine applications.