TY - JOUR

T1 - Dynamics of order parameters of nonstoquastic Hamiltonians in the adaptive quantum Monte Carlo method

AU - Arai, Shunta

AU - Ohzeki, Masayuki

AU - Tanaka, Kazuyuki

N1 - Funding Information:
M.O. was supported by KAKENHI Grants No. 15H0369, No. 16H04382, and No. 16K13849, ImPACT, and JST-START. K.T. was supported by JSPS KAKENHI (Grant No. 18H03303). This work was partly supported by JST-CREST (Grant No. JPMJCR1402).
Publisher Copyright:
© 2019 authors. Published by the American Physical Society.

PY - 2019/3/14

Y1 - 2019/3/14

N2 - We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic p-spin model with infinite-range interactions. The p-spin model has a first-order phase transition for p>2. In the case of p≥5, the p-spin model with antiferromagnetic XX interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a nonstoquastic Hamiltonian, resulting in a negative sign problem. To simulate the p-spin model with antiferromagnetic XX interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the antiferromagnetic XX interaction as fluctuations of the transverse magnetic field. A previous study [J. Inoue, J. Phys. Conf. Ser. 233, 012010 (2010)1742-659610.1088/1742-6596/233/1/012010] derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method, and we verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

AB - We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic p-spin model with infinite-range interactions. The p-spin model has a first-order phase transition for p>2. In the case of p≥5, the p-spin model with antiferromagnetic XX interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a nonstoquastic Hamiltonian, resulting in a negative sign problem. To simulate the p-spin model with antiferromagnetic XX interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the antiferromagnetic XX interaction as fluctuations of the transverse magnetic field. A previous study [J. Inoue, J. Phys. Conf. Ser. 233, 012010 (2010)1742-659610.1088/1742-6596/233/1/012010] derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method, and we verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

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U2 - 10.1103/PhysRevE.99.032120

DO - 10.1103/PhysRevE.99.032120

M3 - Article

C2 - 30999397

AN - SCOPUS:85063272592

VL - 99

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

M1 - 032120

ER -