### Abstract

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.

Original language | English |
---|---|

Article number | 054006 |

Journal | journal of the physical society of japan |

Volume | 88 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*88*(5), [054006]. https://doi.org/10.7566/JPSJ.88.054006

**Quantum phase transition in fully connected quantum Wajnflasz–Pick model.** / Seki, Yuya; Tanaka, Shu; Kawabata, Shiro.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 88, no. 5, 054006. https://doi.org/10.7566/JPSJ.88.054006

}

TY - JOUR

T1 - Quantum phase transition in fully connected quantum Wajnflasz–Pick model

AU - Seki, Yuya

AU - Tanaka, Shu

AU - Kawabata, Shiro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067248659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067248659&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.88.054006

DO - 10.7566/JPSJ.88.054006

M3 - Article

AN - SCOPUS:85067248659

VL - 88

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 5

M1 - 054006

ER -