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Quantum Monte Carlo for Metals

The computer time, in seconds, required for a time step in quantum monte carlo using either extended orbitals taken from a density functional theory (dft) calculation.
The computer time, in seconds, required for a time step in Quantum Monte Carlo using either extended orbitals taken from a density functional theory (DFT) calculation, using these orbitals after they have been transformed into localized orthogonal Wannier orbitals, or after they have been transformed into localized non-orthogonal orbitals versus the number of electrons in the system. These orbitals occur in the determinants of the many-body trial function. With extended orbitals the computer time scales as the cube of the number of electrons, while with localized orbitals the computer time scales linearly with the number of electrons.

Hood, Pask, DuBois, Sadigh

In this project we are developing a highly accurate, first principles computational capability to calculate defect formation energies and the equation of state (EOS) of metallic systems. We are using a newly developed algorithm that enables the study of metallic systems with quantum Monte Carlo (QMC) methods. To date, technical limitations have restricted the application of QMC methods to semiconductors, insulators and the homogeneous electron gas. Using a new formulation based on optimized, non-orthogonal orbitals we have overcome these limitations.[1,2] Using this new "QMC for metals" approach we are determining, for the first time, the significance of correlation effects in the EOS and in the formation energies of point defects, impurities, surfaces and interfaces in metallic systems. These calculations go beyond the state-of-the-art accuracy which is currently obtained with Density Functional Theory (DFT) approaches. These benchmark calculations will provide more accurate predictions for the EOS and the formation energies of vacancies and interstitials in simple metals. These are important parameters in determining the mechanical properties as well as the micro-structural evolution of metals in irradiated materials or under extreme conditions. Furthermore, we plan to study, for the first time, electron correlations in a model system close to the metal-insulator transition point with a parameter-free theory.

References

  1. A.J. Williamson, R.Q. Hood, and J.C. Grossman Linear-Scaling Quantum Monte Carlo Calculations, Phys. Rev. Lett. 87, 246406 (2001).
  2. F. A. Reboredo and A. J. Williamson, Optimized nonorthogonal localized orbitals for linear scaling quantum Monte Carlo calculations , Phys. Rev. B 71, 121105 (2005).

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