This is an open source implementation of the worm algorithm for sign-positive models as explained in our preprint arXiv:2204.12262. Please refer to the main text for an in-depth discussion of the method, particularly the algorithm and the updates. This README focuses on the technical details in order to run the codes and reproduce the data shown in the figures of the main text.

There are 5 directories in this repo

• paper : contains the pdf of the accompanying paper plus the data used to generate the figures in the paper.
• src : the source code of the worm algorithm
• parameter_files : examples of parameter files for Bose-Hubbard and spin-XXZ models.
• test_mpi : parameter files to test the code against ground state Lanczos results for small system sizes.
• tools : simple helper python scripts to extract information from the output hdf5 files

These codes are based on the ALPSCore library. Refer to their website for installation instructions. At the time of this writing, ALPSCore imposed the following system requirements:

• C++ compiler, along with suitable MPI wrappers (e.g. OpenMPI)
• CMake build system (version 3.1 or later),
• Boost headers and program_options library (version 1.56 or later),
• HDF5 library version 1.8.x (version 1.10 does not work, see below).

Beyond these, our codes require

• a C++11-capable compiler. We have only tested our code when ALPSCore is installed with modern compilers that have C++11 features turned on by default.

Detailed instructions on how to build ALPSCore can be fournd in the project's wiki. The procedure revolves around the following:

$ cd alpscore
$ mkdir build.tmp && cd build.tmp
$ cmake ..
$ make -jN
$ make test
$ make install

Replace N with the number of processors you want to use to build, e.g. -j8. You may want to specify additional flags to cmake:

• -DCMAKE_INSTALL_PREFIX=$HOME/.local, or another custom install location. This is required if you don't have permission to write at the default install prefix (/usr/local). Mind that ALPSCore installs a CMake script that has to be picked up by CMake when building our codes. Thus, any non-standard install location needs to be matched by a -DCMAKE_PREFIX_PATH=<...> flag when configuring the client code.
• If a local version of boost has been installed (see above), point CMake to it by specifying -DBOOST_ROOT=/path/to/boost/install. Otherwise your local version may not be found, or be shadowed by an incompatible version.
• We strongly recommend using a recent compiler that has (at least) C++11 features turned on by default.

Our codes also use CMake to configure the build environment. The procedure is analogous to ALPSCore's, e.g.:

$ mkdir build && cd build
$ cmake ../src
$ make -jN all

Again, provide -DCMAKE_PREFIX_PATH=/path/to/alpscore/install if ALPSCore has been installed in a non-standard location. Refer to the READMEs in the subdirectories of the individual codes for additional flags to customize their behavior.

Simulation parameters may be specified in an INI-style parameter file, e.g.

sweeps = 1000000
thermalization = 10000
timelimit = 18000

followed by simulation-specific parameters. The parameter files which have been use to produce some of the figures in the main text are provided in the parameter_files subdirectory of the individual codes. Assuming this file is saved as job.ini, the simulation is started by running :

$ ./qmc_worm job.ini

which would run it on a single core. After an initial thermalization phase of 10000 sweeps, the code would run for another one million sweeps while measuring the observables after each one. The code would run for at most 5 hours (=18000 seconds), which is useful when working on a cluster with wallclock constraints. A timelimit of 0 means that no time limit is imposed at all.

When the desired number of sweeps has been performed or the job ran out of time, the results are written to job.out.h5.

To run the simulation on multiple cores or even nodes, use the executable without the _single suffix in combination with the MPI wrapper script:

$ mpiexec -n $NUM_MPI ./qmc_worm_mpi job.ini

This will start $NUM_MPI independent simulations with identical parameters (with the exception of the random seed: each MPI process uses its own RNG, seeded with the SEED parameter plus its MPI rank).

Each MPI process will produce independent checkpoint files, enumerated by the MPI rank, e.g. job.clone.h5.<RANK>, but only one output file job.out.h5 will be written which contains the collected results from all MPI processes.

Periodically, the total number of measurements among all the processes will be accumulated. If it exceeds the value specified in the sweeps parameter (or the timelimit is reached), the simulation will terminate. Since this check requires synchronization of the processes, it is not done after each sweep but rather at intervals between Tmin and Tmax seconds (which may be specified in the parameters file). Thus, when working on a cluster with wallclock constraints, one should reserve at least timelimit+Tmax seconds to avoid premature forceful termination of the job.

Keep in mind that the thermalization phase has to be done for each MPI process independently, i.e. $NUM_MPI × thermalization sweeps will be carried out in total before measurement samples can be taken.

The complete list of all configurable parameters can be obtained by calling the executables with the --help flag:

$ ./qmc_worm --help
# Simulation of the Bose-Hubbard or the XXZ model with the worm algorithm
[...]
Available options:
   help (bool):                         Print help message
   SEED (long int):                     PRNG seed (default value: 42)
   timelimit (unsigned long int):       time limit for the simulation (default value: 0)
   outputfile (std::string):            name of the output file (default value: qmc_worm.out.h5)
   checkpoint (std::string):            name of the checkpoint file to save to (default value: qmc_worm.clone.h5)

[...]

Most parameters provide default values, but some don't to force the user to consciously specify them.

Any parameter may be overridden on the command line, e.g.

$ ./qmc_worm job.ini --sweeps=10000

Parameters provided on the command line take precedence over those in the parameter file or in the parameters stored in a checkpoint (see below).

In case the simulation terminated because it reached the timelimit, or the job terminated due to e.g. a node failure, one can resume the simulation from the checkpoint:

$ ./qmc_worm job.clone.h5

In case MPI is used, any one checkpoint file can be specified on the command line and the individual MPI processes will find their respective checkpoint file automatically:

$ mpiexec -n $NUM_MPI ./qmc_worm.clone.h5

However, $NUM_MPI needs to match the amount used in the previous run.

When resuming, the timelimit is basically reset. ~~In case the simulation terminated because it had taken sweeps measurements but the results turned out unsatisfactory, one can override the sweeps parameter on the command line to sample further:

$ ./qmc_worm job.clone.h5 --sweeps=10000000

Not all parameters can be overridden when resuming from a checkpoint this way.

Simulation results are output in a HDF5 data file job.out.h5 containing the simulation parameters, measurements of the observables along with binning analyses. This file follows the standard format used in the example codes of the ALPSCore project; please refer to their documentation for details.

These codes make use of the ALPSCore library, based on the original ALPS project. ALPSCore makes use of the HDF5 data format, as well as the Boost C++ libraries. We also rely on some functionality of the Froehlich polaron lecture notes and code, and on the TKSVM library.

There are a number of open-source software packages available for quantum Monte Carlo simulations. Here we list some of them. The list is non-exhaustive and we will be happy to add yours provided it qualifies:

• Applications and Libraries for Physics Simulations: ALPS -- currently down and no longer maintained
• The Core libraries of the previously mentioned ALPS project, and which are used in this project: ALPSCore
• A portal Site of Material Science Simulations: MateriApps
• Algorithm for Lattice Fermions: ALF
• Project for advancement of software usability in materials science(PASUMS): 2DMAT
• Directed worms in the continuous time path integral representation for a S=1/2 antiferromagnetic Heisenberg chain in a longitudinal field: worms
• Toolbox for Research on Interacting Quantum Systems: TRIQS
• The Machine-Learning toolbox for Quantum Physics: Netket
• The tensorial Kernel Support vector Machine project for interpretation and classification of classical Monte Carlo spin systems: TKSVM

Copyright © 2022 Nicolas Sadoune and Lode Pollet

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

A copy of the GNU General Public License is available in the file LICENSE.txt.