We construct a quantum Wajnflasz–Pick model that is a generalized quantum Ising model, and investigate the nature of quantum phase transitions of the model with infinite-range interactions. 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 adiabatic quantum computation (AQC). We add a quantum driver Hamiltonian to the Hamiltonian of the classical Wajnflasz–Pick model. The classical Wajnflasz–Pick model consists of two-level systems as with the usual Ising model. Unlike the usual Ising spin, each of the upper and lower levels of the system can be degenerate. The states in the upper and lower levels are referred to as the upper and lower states, respectively. The quantum driver Hamiltonian that we introduced causes spin flip between the upper and lower states and state transitions within each of the upper and lower states. Numerical analysis showed that the model undergoes first-order phase transitions, whereas a corresponding quantum Ising model, the quantum Curie–Weiss model, does not undergo first-order phase transitions. In particular, we observed an anomalous phenomenon that the system undergoes successive first-order phase transitions under certain conditions. The obtained results indicate that the performance of QA and AQC by using degenerate two-level systems can be controlled by adjusting the parameters in the systems.
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