Control of Phase Transitions in Wajnflasz–Pick model

We construct a quantum Wajnflasz–Pick model, and investigate a nature of quantum phase transitions of the model. Quantum phase transition phenomena have drawn attention in the field of quantum computing as well as condensed matter physics, since the phenomena are closely related to the performance of quantum annealing (QA) and quantum adiabatic computation (QAC). Adding a driver Hamiltonian that causes spin flip and state transitions within upper and lower states to the Hamiltonian of classical Wajnflasz–Pick model, we construct the quantum model where phase transitions are controllable. Numerical analysis showed that the model undergoes first-order phase transitions whereas a corresponding spin-1/2 model does not undergo first-order phase transitions. In particular, we observed an anomalous phenomenon that the system undergoes first-order phase transitions twice under certain conditions. The results indicate that the performance of QA and QAC can be affected by the choice of the number of upper and lower states and the parameter in the driver Hamiltonian.