Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model

We study the threshold temperature for pairwise thermal entanglement in the spin-1/2 isotropic Heisenberg model up to 11 spins and find that the threshold temperature for odd and even number of qubits approaches the thermal dynamical limit from below and above, respectively. The threshold temperature in the thermodynamical limit is estimated. We investigate the many-particle entanglement in both the ground states and the thermal states of the model up to 11 spins, and find that the ground state in the four-qubit model is a four-particle entangled state and the corresponding thermal state is also a four-particle entangled state before a threshold temperature