Three-Spin System in the Presence of the Quantum Cluster Interaction

We consider a three-spin system under Heisenberg and quantum cluster interactions. Firstly, by focusing on the entanglement between each pair of them at zero temperature, we show that where the quantum phase transition (QPT) of the infinite-size system might happen can be observed even for a such finite spin system. In fact, where the QPT happened, the ground state of the mentioned three-spin system will become the W-state, which is the main reason of possibility of detecting the place of an infinite-size system. Secondly, we investigate the thermal entanglement and show that corresponding to the temperature increase, the mentioned point goes toward the larger exchange coupling constant values, whereas the amount of entanglement decreases, that the latter meets our expectation. Then by using the one-tangle method, we show that at zero temperature, QPT is taken place at the same point. Finally, by using the logarithmic negativity measure, we investigate the role of thermal fluctuations on the previously mentioned finite spin system.