In this example, we will demonstrate using Rimu with MPI. A runnable script is located at here. Run it as mpirun julia BHM-example.jl.

We start by importing Rimu and Rimu.RMPI, which contains MPI-replated functionality.

using Rimu
using Rimu.RMPI

We will compute the ground-state of a Bose-Hubbard model in momentum space with 10 particles in 10 sites.

First, we define the Hamiltonian. We want to start from an address with zero momentum.

address = BoseFS((0, 0, 0, 0, 10, 0, 0, 0, 0, 0))

BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0))

We will set the interaction strength u to 6. The hopping strength t defaults to 1.0.

hamiltonian = HubbardMom1D(address; u=6.0)

HubbardMom1D(BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0)); u=6.0, t=1.0)

Next, we construct the starting vector. Wrap a vector in MPIData to make it MPI distributed. We set the vector's style to IsDynamicSemistochastic, which improves statistics and reduces the sign problem.

dvec = MPIData(DVec(address => 1.0; style=IsDynamicSemistochastic()))

MPIData(DVec) with 1 entries, style = IsDynamicSemistochastic{Float64, true}(1.0, Inf, 1.0), strategy = MPIPointToPoint
  BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0)) => 1.0

We set a reporting strategy. We will use ReportToFile, which writes the reports directly to a file. This is useful for reducing memory use in long-running jobs, as we don't need to keep the results in memory. Setting save_if=is_mpi_root() will ensure only the root MPI rank will write to the file. The chunk_size parameter determines how often the data is saved to the file.

r_strat = ReportToFile(filename="result.arrow", save_if=is_mpi_root(), chunk_size=1000)

ReportToFile
  filename: String "result.arrow"
  chunk_size: Int64 1000
  save_if: Bool true
  return_df: Bool false
  io: IOContext{Base.PipeEndpoint}

Now, we can set other parameters as usual. We will perform the computation with 10_000 walkers. We will also compute the projected energy.

s_strat = DoubleLogUpdate(targetwalkers=10_000)
post_step = ProjectedEnergy(hamiltonian, dvec)

ProjectedEnergy{HubbardMom1D{Float64, 10, BoseFS{10, 10, BitString{19, 1, UInt32}}, 6.0, 1.0}, Rimu.DictVectors.FrozenDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}, Rimu.DictVectors.FrozenDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}}(:vproj, :hproj, HubbardMom1D(BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0)); u=6.0, t=1.0), Rimu.DictVectors.FrozenDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}(Pair{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}[BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0)) => 1.0]), Rimu.DictVectors.FrozenDVec{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}(Pair{BoseFS{10, 10, BitString{19, 1, UInt32}}, Float64}[BoseFS{10,10}((1, 0, 0, 0, 8, 0, 0, 0, 1, 0)) => 5.692099788303083, BoseFS{10,10}((0, 0, 0, 0, 8, 0, 0, 0, 0, 2)) => 4.024922359499621, BoseFS{10,10}((0, 0, 0, 0, 10, 0, 0, 0, 0, 0)) => 7.0, BoseFS{10,10}((0, 0, 1, 0, 8, 0, 1, 0, 0, 0)) => 5.692099788303083, BoseFS{10,10}((0, 0, 0, 1, 8, 1, 0, 0, 0, 0)) => 5.692099788303083, BoseFS{10,10}((0, 1, 0, 0, 8, 0, 0, 1, 0, 0)) => 5.692099788303083]))

Finally, we can run the computation. The @mpi_root macro performs an action on the root rank only, which is useful for printing.

lomc!(hamiltonian, dvec; r_strat, s_strat, post_step, dτ=1e-4, laststep=10_000)
@mpi_root println("Finished!")

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