Entropy, entanglement and susceptibility of three qubits near quantum criticality

Abstract: This work investigates 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 thermodynamics of the system by calculating its magnetic susceptibility and analyzing how this quantity encodes information about entanglement. By deriving rigorous bounds for susceptibility, we demonstrate that their violation serves as an entanglement witness. Our results show that anisotropy enhances entanglement, extending the temperature range over which it persists. Additionally, by tracing over the degrees of freedom of two qubits, we examine the reduced density matrix of the remaining qubits and find that its entropy under the influence of the magnetic field can be mapped to an effective thermal bath at $(B,K) > 0$ K.