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Quantum Phase Transition in Fully-Connected Quantum Wajnflasz-Pick Model | | Yuya Seki
; Shu Tanaka
; Shiro Kawabata
; | | Date: |
8 Jan 2019 | | Abstract: | We construct a quantum Wajnflasz-Pick model that is a generalized quantum
Ising model, and investigate a 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 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 the lower levels of
the system can be degenerate. The states in the upper level and the lower level
are referred to as upper states and lower states, respectively. The quantum
driver Hamiltonian we introduced causes spin flip between the upper and the
lower states and state transitions within each of the upper and the lower
states. Numerical analysis showed that the model undergoes first-order phase
transitions whereas a corresponding quantum Ising model, 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 the parameters in the systems. | | Source: | arXiv, 1901.2242 | | Services: | Forum | Review | PDF | Favorites | |
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