Entropy, entanglement, and susceptibility of three qubits near quantum criticality

In this work, we investigate a system of three entangled qubits within the XXX model, subjected to an external magnetic field in the z direction and incorporating an anisotropy term along the y axis. We explore the system's thermodynamics by calculating its magnetic susceptibility and analyzing how this quantity encodes information about entanglement. By deriving rigorous bounds for the susceptibility, we demonstrate that violations of these bounds serve as an entanglement witness. Our results show that anisotropy enhances entanglement, extending the temperature range over which it persists. Furthermore, when the system is traced over the degrees of freedom of two qubits, the reduced entropy of the remaining single qubit corresponds to that of a system in a thermal bath with temperature T>0K.