Quantum Monte Carlo for the harmonic oscillator
Jupyter python notebooks highlighting two ground state (T=0) methods:
- Variational Monte Carlo (VMC)
- Path Integral Ground State Monte Carlo (PIGS)
These codes were originally written as part of a series of lectures presented at the 2018 National Magnet Lab Winter Theory School and are intended to be pedagogical at the expense of any and all efficiency. These should be treated as toy codes. Statistical uncertainties are approximated via the standard error and ignore all correlations between measurements. These are likely to underestimate the error in the data.
PDF of slides from the Winter School can be found here:
For more information on PIGS please see:
- M. Ceperley, Path Integrals in the Theory of Condensed Helium, Rev. Mod. Phys. 67, 279 (1995).
- A. Sarsa, K. E. Schmidt, and W. R. Magro, A Path Integral Ground State Method, J. Chem. Phys. 113, 1366 (2000).
- J. E. Cuervo, P.-N. Roy, and M. Boninsegni, Path integral ground state with a fourth-order propagator: Application to condensed helium, Chem. Phys. 122, 114504 (2005).
- Y. Yan and D. Blume, Path Integral Monte Carlo Ground State Approach: Formalism, Implementation, and Applications, J. Phys. B: Atom., Mol., and Opt. 50, 223001 (2017).
The creation of these training materials was supported in part by the National Science Foundation under Award No. DMR-1553991.
