This library provides tool to simulate a pure gauge SU(3) theory on a lattice. It aimed to provide generic tool such that many different simulation or methods can be used.
You can easily choose the Monte Carlo algorithm, you can implement you own Hamiltonian etc. It provides also an easy way to do simulation in dimension between 1 and usize::MAX. So this library is not limited to d = 3 or d = 4.
Check out my other repo plaquette, a set of simulation binary I used for my research.
Features:
- Generic dimension;
- Configurable Monte Carlo algorithm;
- Multi Platform;
- Configurable Hamiltonian;
- Serde support;
- Native rust;
- Some statistical tools;
Not yet implemented features:
- More statistical tools;
- Fermion support;
- SU(N) support;
- Config file;
- C friendly API / ABI;
Add lattice_qcd_rs = { version = "0.2.1", git = "https://github.com/ABouttefeux/lattice_qcd_rs" } into your cargo.toml.
The set of features are
serde-serializeon by default permit the use of serde on some structureno-overflow-testusage interns to desable overflow test for coverage.
At the moment it is not on crates.io. Maybe I will add it. But for the moment it is still in development.
Note that you may want to specify a specific commit as for now I may introduce breaking changes.
I will however commit to more stability once I am ready to release version 0.2.0.
First let us see how to do a simulation on a 10x10x10x10 lattice with beta = 1. We are looking to compute 1/3 <Re(Tr(P_{ij}))> the trace of all plaquette after a certain number of steps. In our cases Beta is small so we choose 100'000 steps.
extern crate lattice_qcd_rs as lq;
extern crate rand_xoshiro;
use lq::prelude::*;
# use std::error::Error;
# fn main() -> Result<(), Box<dyn Error>> {
let mut rng = rand_xoshiro::Xoshiro256PlusPlus::from_entropy();
let size = 1000_f64;
let number_of_pts = 10;
let beta = 1_f64;
let mut simulation =
LatticeStateDefault::<4>::new_determinist(size, beta, number_of_pts, &mut rng)?;
let spread_parameter = 0.1_f64;
let mut mc = MetropolisHastingsDeltaDiagnostic::new(spread_parameter, rng)?;
for _ in 0..100 {
for _ in 0..1_000 {
simulation = simulation.monte_carlo_step(&mut mc)?;
}
// the more we advance te more the link matrices
// will deviate form SU(3), so we reprojet to SU(3)
// every 1_000 steps.
simulation.normalize_link_matrices();
}
let average = simulation.average_trace_plaquette().ok_or(ImplementationError::Unreachable)?.real() / 3_f64;
# Ok(())
# }This library use rayon as a way to do some computation in parallel. However not everything can be parallelized. I advice that if you want to do multiple similar simulation (for instance you want to do for Beta = 1, 1.1, 1.2, ...) to use rayon. In order to do multiple parallel simulation.
Looking for more concrete example ? Check out my other repo plaquette. It contain the binary I use for my research.
implement the trait LatticeState.
If you want to use your own state with the hybride Monte Carlo
you will have to implement
LatticeStateWithEField for LatticeStateEFSyncDefault<YourState>
I provide two algorithm: Metropolis Hastings and hybride Monte Carlo
Look at the traits MonteCarlo,
or alternatively MonteCarloDefault.
MonteCarloDefault can be easier to implement but note that the entire Hamiltonian is computed each time we do step for the previous and the new one which can be slower to compute the delta Hamiltonian.
To use a MonteCarloDefault as a MonteCarlo there is a wrapper: MCWrapper.
This some code for my PhD thesis. Mainly I use arXiv:0707.2458, arXiv:0902.28568 and arXiv:2010.07316 as a basis.
The goal is to provide an easy to use, fast and safe library to do classical lattice simulation.
This library use the trait rand::RngCore any time a random number generator.
The choice of RNG is up to the user of the library. However there is a few trade offs to consider.
Let us break the different generator into categories. For more details see https://rust-random.github.io/book/guide-gen.html.
Some of the possible choice :
- Recomanded
rand_xoshiro::Xoshiro256PlusPlusNon-cryptographic. It has good performance and statistical quality, reproducible, and has usefuljumpfunction. It is the recommended PRNG. rand::rngs::ThreadRnga CSPRNG. The data is not reproducible and it is reseeded often. It is however slow.rand::rngs::StdRngcryptographic secure, can be seeded. It is determinist but not reproducible between platform. It is however slow.rand_jitter::JitterRngTrue RNG but very slow.
Also ranlux is a good choice. But there is no native rust implementation of it that I know of (except mine but it is very slow).
use lattice_qcd_rs::{
error::ImplementationError,
ComplexField,
simulation::monte_carlo::MetropolisHastingsDeltaDiagnostic,
simulation::state::{LatticeState, LatticeStateDefault},
};
# use std::error::Error;
# fn main() -> Result<(), Box<dyn Error>> {
let mut rng = rand::thread_rng();
let size = 1_000_f64;
let number_of_pts = 4;
let beta = 2_f64;
let mut simulation =
LatticeStateDefault::<4>::new_determinist(size, beta, number_of_pts, &mut rng)?;
let spread_parameter = 1E-5_f64;
let mut mc = MetropolisHastingsDeltaDiagnostic::new(spread_parameter, rng)
.ok_or(ImplementationError::OptionWithUnexpectedNone)?;
let number_of_sims = 100;
for _ in 0..number_of_sims / 10 {
for _ in 0..10 {
simulation = simulation.monte_carlo_step(&mut mc)?;
}
simulation.normalize_link_matrices(); // we renormalize all matrices back to SU(3);
}
let average = simulation.average_trace_plaquette()
.ok_or(ImplementationError::OptionWithUnexpectedNone)?
.real();
# Ok(())
# }Alternatively other Monte Carlo algorithm can be used like,
use lattice_qcd_rs::{
error::ImplementationError,
simulation::monte_carlo::{McWrapper, MetropolisHastingsDiagnostic},
simulation::state::{LatticeState, LatticeStateDefault},
};
# use std::error::Error;
# fn main() -> Result<(), Box<dyn Error>> {
let mut rng = rand::thread_rng();
let size = 1_000_f64;
let number_of_pts = 4;
let beta = 2_f64;
let mut simulation =
LatticeStateDefault::<3>::new_determinist(size, beta, number_of_pts, &mut rng)?;
let number_of_rand = 20;
let spread_parameter = 1E-5_f64;
let mut mc = McWrapper::new(
MetropolisHastingsDiagnostic::new(number_of_rand, spread_parameter)
.ok_or(ImplementationError::OptionWithUnexpectedNone)?,
rng,
);
simulation = simulation.monte_carlo_step(&mut mc)?;
simulation.normalize_link_matrices();
# Ok(())
# }or
use lattice_qcd_rs::{
integrator::SymplecticEulerRayon,
simulation::monte_carlo::HybridMonteCarloDiagnostic,
simulation::state::{LatticeState, LatticeStateDefault},
};
# use std::error::Error;
# fn main() -> Result<(), Box<dyn Error>> {
let mut rng = rand::thread_rng();
let size = 1_000_f64;
let number_of_pts = 4;
let beta = 2_f64;
let mut simulation =
LatticeStateDefault::<3>::new_determinist(size, beta, number_of_pts, &mut rng)?;
let delta_t = 1E-3_f64;
let number_of_step = 10;
let mut mc =
HybridMonteCarloDiagnostic::new(delta_t, number_of_step, SymplecticEulerRayon::new(), rng);
simulation = simulation.monte_carlo_step(&mut mc)?;
simulation.normalize_link_matrices();
# Ok(())
# }
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