期刊
PHYSICAL REVIEW E
卷 105, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.105.065302
关键词
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资金
- U.C. National Laboratory In-Residence Graduate Fellowship through the U.C. National Laboratory Fees Research Program
- center of Materials Theory as a part of the Computational Materials Science (CMS) program - U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division
- U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-SC0022311]
- U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship [DE-SC0020347]
- U.S. Department of Energy (DOE) [DE-SC0022311] Funding Source: U.S. Department of Energy (DOE)
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. These methods can greatly accelerate the simulations and improve computational efficiency.
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat ???stiffness??? arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.
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