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PolaronQMC.jl

Initially a Path Integral Monte-Carlo code for Polarons in the Julia programming language. A work in progress!

References

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

Lectures and other notes (including finite T PIMC)

[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/

Other codes

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

Packages

Lattice-based Ising MC + AFQMC - https://github.com/crstnbr/MonteCarlo.jl

Potential outputs

Observables:

  • Energy (Various estimators)
  • Correlation function

Errors (on observables)

  • Jack knife errors
  • Bin based errors

Debugging/System information

  • Attempted number of moves for different movers
  • Acceptance ratios

HALCYON - PIGS might fly

Initially a Path Integral Monte-Carlo code for Polarons in the Julia programming language. A work in progress!

References

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

Lectures and other notes (including finite T PIMC)

[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/

Other codes

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

Packages

Lattice-based Ising MC + AFQMC - https://github.com/crstnbr/MonteCarlo.jl