Writing a Path Integral Monte-Carlo code in the Julia programming language. A work in progress!
Halcyon.jl is a research code to look at combining Path Integrals with Gaussian Process inference. The hope (as always!) is to somehow avoid the sign error, here by seeing whether an extended version of the Feynman variational method can be used, possibly with some kind of quantised form of Gaussian Process.
Textbook: "Interacting Electrons: Theory and Computational Approaches" Richard M. Martin, Lucia Reining, and David M. Ceperley. Cambridge University Press. (2016) Section 25.4 (Ground-state path integrals (GSPI)) http://dx.doi.org/10.1017/CBO9781139050807
PIGS papers:
[1] "Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations" Stefano Baroni and Saverio Moroni Phys. Rev. Lett. 82, 4745 (1999); http://dx.doi.org/10.1103/PhysRevLett.82.4745
[2] "Path integrals in the theory of condensed helium" D. M. Ceperley Rev. Mod. Phys. 67, 279 (1995); http://dx.doi.org/10.1103/RevModPhys.67.279
[3] A path integral ground state method A. Sarsa, K. E. Schmidt and W. R. Magro J. Chem. Phys. 113, 1366 (2000); http://dx.doi.org/10.1063/1.481926
Fermion sign problem papers:
[1] Sign problem in the numerical simulation of many-electron systems E. Y. Loh, Jr., J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar Phys. Rev. B 41, 9301 – Published 1 May 1990 https://doi.org/10.1103/PhysRevB.41.9301
[2] Monte Carlo simulations with indefinite and complex-valued measures T. D. Kieu and C. J. Griffin Phys. Rev. E 49, 3855 – Published 1 May 1994 https://doi.org/10.1103/PhysRevE.49.3855
[2021Ceperley] CECAM talk by David Ceperley, very clear and nice high res slides. https://www.youtube.com/watch?v=R0stKun1w0A
2012 - quantum Monte Carlo: Theory and Fundies - Uni of illinois http://www.mcc.uiuc.edu/summerschool/2012/program.html
Ethan W. Brown's 2014 Thesis - warm dense matter: https://www.ideals.illinois.edu/bitstream/handle/2142/50560/Ethan_Brown.pdf?sequence=1
2013 Workshop with a half-dozen path integral talks (Ceperley, Boninsegni, Brown, etc. - unfortunately Clark's video has broken sound!) http://www.int.washington.edu/talks/WorkShops/int_13_2a/
Python - BryanClark: Tutorial: Writing a Path Integral Code in Python http://web.engr.illinois.edu/~bkclark/PIMCTutorial/tutorial.pdf
Python - Adrian Del Maestro - 14 pages of notes and a beautifully clean 222 line PIMC Python code for a 1D SHO https://github.com/agdelma/pimc-notes
Julia - Minimal harmonic-oscillator PIMC implementation https://nbviewer.jupyter.org/github/Paul-St-Young/share/blob/master/julia-tutorial-pimc/python_vs_julia/julia-pimc.ipynb
C++ - PIMC++: finite T PIMC code, originally by Bryan Clark and Ken Esler, with more recent contributions by Ethan Brown: https://github.com/bkclark/pimcpp
C++ - Ethan Brown now has his own 'Simple PIMC' code: https://github.com/etano/simpimc
F90 See also, @amaciarey's F90 PIGS code, for dipolar bosons in 2D: https://github.com/amaciarey/PathIntegralGroundState
C++ John Shumway's (now abandoned) C++ code for quantum dots etc. : http://phys-tools.github.io/pi-qmc/ https://github.com/phys-tools/pi-qmc
Lattice-based Ising MC + AFQMC - https://github.com/crstnbr/MonteCarlo.jl