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6. Hubbard model on a honeycomb lattice

6.1. Set up the Hamiltonian

# setup scratch dir
from pathlib import Path
from tutorial_utils import run_afqmc

scratch_dir = Path("data")
scratch_dir.mkdir(parents=True, exist_ok=True)

# setup the Hamiltonian
import numpy as np

from afqmctools.systems.lattice import get_lattice
from afqmctools.utils.visualize import plot_lattice
from afqmctools.hamiltonian.model.director import HamiltonianDirector
import afqmctools.utils.io as io

lattice = get_lattice(
    params=dict(
        L1 = 4,
        L2 = 4,
        boundary1 = "pbc",
        boundary2 = "pbc",
        type = "honeycomb"
    )
)

# plot the lattice for reality checks!
plot_lattice(lattice)

# define Hamiltonian parameters
hamiltonian_params = {
    'U': 6.0
}

params = {
    'hamiltonian': hamiltonian_params
}

# make the Hamiltonian
hamiltonian = HamiltonianDirector(
    source=params,
    lattice=lattice
).build()

# save for AFQMC
io.write_model_hamiltonian(hamiltonian,fname=scratch_dir/"afqmc.h5")

# run autoHF and save wavefunction as trial wavefunction
from autohf import lattice_hf
from autohf.hamiltonian import AutoHFHamiltonian
from afqmctools.inputs.from_autohf import autohf_to_afqmc

# Typically, we want to use a Ueff to generate a trial wavefunction
#    since HF's critical U is lower than the correct critical U
Ueff = 3.0

# define effective Hamiltonian parameters
hamiltonian_params = {
    'U': Ueff
}

params = {
    'hamiltonian': hamiltonian_params
}

# make the Hamiltonian
effective_hamiltonian = HamiltonianDirector(
    source=params,
    lattice=lattice
).build()

# convert afqmctools Hamitlonian to AutoHFHamiltonian
autohf_hamiltonian = AutoHFHamiltonian(effective_hamiltonian)

# set the number of electrons!!
nelec=(16-1,16-1)

settings = dict(
    ansatz = 'SD_ROT',
    numSteps = 100,
    nelec = nelec,
    numTrials = 100,
    seed = 42
)

results = lattice_hf(hamiltonian=autohf_hamiltonian,settings=settings)

autohf_to_afqmc(results,output_fname=scratch_dir/"afqmc.h5")

6.2. Write input file

For more information about the input file, see Understanding the input file.

from afqmctools.inputs.from_hdf import write_json

# write input file
afqmc_execution_options = {
    "timestep": 0.01,
    "steps": 10000,
    "accumlate_interval": 10,           # in units of steps
    "measure_interval": 10,             # in units of steps
    "population_control_interval" : 10, # in units of steps
    "walker_ortho_interval" : 10 ,      # in units of steps
    "n_walkers_per_mpi_task": 100,
    "seed" : 42
}

write_json(
    scratch_dir/ "afqmc.json",
    fwfn0=scratch_dir / "afqmc.h5",
    exec_opts=afqmc_execution_options
)

6.3. run AFQMC

# run SAFIRE
run_afqmc(
    run_dir=scratch_dir,
    run_mode="local_cpu",
    input_file="afqmc.json",
    np=16,             # number of MPI tasks
    output_file=None   # optionally direct output to file instead of here
)

6.4. Analyze the results

# analyze results
from stats.scalar_dat import analyze_scalar_data

_ = analyze_scalar_data(dict(
    fname = scratch_dir/"qmc.s000.scalar.dat",
    xaxis = "time",
    nequil = 5,
    trace = True
))