Edit on GitHub

Rimu.jl Package Guide

Random Integrators for many-body quantum systems

The grand aim is to develop a toolbox for many-body quantum systems that can be represented by a Hamiltonian in second quantisation language. Currently there are tools to find the ground state with a Lanczos algorithm (using KrylovKit.jl for small Hilbert spaces), or with projector quantum Monte Carlo in the flavour of full configuration interaction quantum Monte Carlo (FCIQMC, see References). We will add tools to solve the time-dependent Schrödinger equation and Master equations for open system time evolution.

Installation

Installing Rimu for usage

Rimu can be installed with the package manager directly from the github repository. Hit the ] key at the Julia REPL to get into Pkg mode and type

pkg> add https://github.com/joachimbrand/Rimu.jl

Alternatively, use

julia> using Pkg; Pkg.add(PackageSpec(url="https://github.com/joachimbrand/Rimu.jl"))

in order to install Rimu from a script.

Installing Rimu for development

In order to be able to edit the source code, push changes, change and make new git branches, etc., clone the git repository with git clone to a convenient location, e.g. ~/mygitpackagefolder/. Then hit the ] key at the Julia REPL to get into Pkg mode and type

pkg> develop ~/mygitpackagefolder/rimu.jl

where the file path has to be adjusted to the location of the cloned git repository.

Usage

The package is now installed and can be imported with

julia> using Rimu

When planning to edit the code of the package it is advisable to use the Revise package by issuing

julia> using Revise

before using Rimu. This will track any changes made to the source code of Rimu and the changed package will be available after saving the source code (hopefully, and most of the time, without restarting the Julia REPL).

Rimu offers a number of tools for representing Hamiltonians (see Hamiltonians) and state vectors / wave functions (see DictVectors) as well as algorithms to find the ground state, e.g. lomc!.

Scripts

Rimu is written as a Julia package to be imported with using Rimu as described above. It supplies useful functions and types. Performing actual calculations and analysing the results is done with scripts. The folder scripts/ contains a collections of scripts that are either examples for use of the Rimu package or useful scripts for data analysis. In particular:

  • scripts/BHM-example.jl is an example script that runs fciqmc on the 1D Bose-Hubbard model. A data frame with results is written to the file fciqmcdata.arrow.
  • test/script_mpi_minimum_ptp.jl demonstrates basic usage of Rimu with MPI.

MPI

The Rimu package can run in parallel on different processes or node and distribute work by making use of MPI, or "message passing interface". For example, running

> julia scripts/BHM-example.jl

will run on one processor with the main lomc!() computation (i.e. after package loading and compilation) completing in 2.69 seconds.

Running

> mpirun -np 4 julia scripts/BHM-example-mpi.jl

on the same hardware makes use of 4 cores and the main part completes in 1.04 seconds, a speedup factor of 2.6. This seems reasonable, given that extra work needs to be done for communicating between different processes.

Initialising and finalising MPI communication has to be handled at the script level. Enabling MPI communication for use in lomc!() is done by wrapping the primary data structures as MPIData. The relevant functionality is provided by the module Rimu.RMPI.

See examples in the Scripts folder.

References

The code implements the FCIQMC algorithm described in

  • "Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space", G. H. Booth, A. J. W. Thom, A. Alavi, J. Chem. Phys. 131, 054106 (2009).

Scientific papers using the Rimu code:

  • "Improved walker population control for full configuration interaction quantum Monte Carlo", M. Yang, E. Pahl, J. Brand, J. Chem. Phys. 153, 170143 (2020); DOI: 10.1063/5.0023088; arXiv:2008.01927.
  • "Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo", J. Brand, M. Yang, E. Pahl; arXiv:2103.07800 (2021).