9. Hartree-Fock trial wavefunctions with autoHF#
This example covers generating a Hartree-Fock trial wavefunction using autoHF on a Hubbard model Hamiltonian on square lattice as a test case. We note that autohf can handle general lattice model Hamiltonians just as SAFIRE can.
A lattice model Hamiltonian can be generated using afqmctools and a toml-based input file. Below is a sample input file, which we name input.toml, for a Hubbard model on a 2x3 square lattice with periodic boundary conditions.
[hamiltonian]
t = 1.0 # defaults to 1.0
U = 2.0
[lattice]
L1 = 2
L2 = 3
boundary1 = "PBC" # or "open" for open boundaries
boundary2 = "PBC" # or "open" for open boundaries
[misc_params]
nelec = [2,2]
if no “type” is specified in the “lattice” section, then a square lattice is used.
autohf and afqmctools can be invoked within a Python script as
from afqmctools.hamiltonian.model.director import HamiltonianDirector
import afqmctools.utils.io as io
from autohf import lattice_hf
infile = "input.toml"
# Build and save a lattice model Hamiltonian
hamiltonian_dir = HamiltonianDirector(source=infile)
lattice = hamiltonian_dir.builder.lattice
hamiltonian = hamiltonian_dir.build()
nelec = io.read_input_params(infile)["misc_params"]["nelec"]
io.write_model_hamiltion(
hamiltonian=hamiltonian,
fname="afqmc.h5",
nelec=nelec
)
settings = dict(
ansatz = 'SD_ROT',
numSteps = 100,
output = "afqmc.h5",
nelec = nelec,
numTrials = 10,
seed = 42
)
lattice_hf(
hamiltonian=hamiltonian,
lattice=lattice,
settings=settings
)
If the sample Python script is run above with the sample input file, the following should be present at the end of the output.
-----------------------
- ╔═╗ ------- ╖ ╓╔═╕ --
- ╠═╣ ╖╖╒╦╕╔╗ ╠═╣╠╕ ---
- ╜ ╙ ╚╝ ╜ ╚╝ ╜ ╙╨ ----
-----------------------
===== AutoHF Settings =====
inputfile input.toml
noncollinear False
gpu False
approx_expm False
force_complex False
ansatz SD_ROT
opt_method grad
seed 42
eta 0.1
numSteps 100
numTrials 10
plot False
verbose False
output afqmc.h5
adding flags
[CpuDevice(id=0)]
Reading hopping from spin sector 0
Running in Rotation Mode
Reference HF Energy = -8.5
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-8.85084240088267 [-8.8508028 -8.85081774 -8.85079141 -8.85083354 -8.85077747 -8.8508424
-8.85074155 -8.85072213 -8.85077628 -8.85079785]
-8.850846544507528 [-8.85081272 -8.85082552 -8.85083179 -8.85084326 -8.85078358 -8.85084654
-8.85075374 -8.85073443 -8.85077427 -8.85080331]
-8.85085661657257 [-8.85079829 -8.85083756 -8.85085662 -8.85085299 -8.8507937 -8.85083583
-8.85075698 -8.85075545 -8.85076395 -8.85077926]
-8.850855426798793 [-8.85078645 -8.85084258 -8.85085543 -8.85084409 -8.85081032 -8.85082811
-8.85075928 -8.8507832 -8.85075959 -8.85076095]
-8.850840763614364 [-8.85079073 -8.85083678 -8.85084076 -8.85083078 -8.8508239 -8.85082617
-8.85076312 -8.85081056 -8.85075796 -8.85076171]
-8.850830994280757 [-8.85079902 -8.85082955 -8.85083099 -8.85083079 -8.85082299 -8.85082425
-8.85076817 -8.85082445 -8.85075197 -8.85076466]
-8.850839901609366 [-8.85079786 -8.85082657 -8.85082912 -8.8508399 -8.85081279 -8.8508236
-8.85076499 -8.85082191 -8.85075483 -8.85076488]
-8.850847759374995 [-8.85080281 -8.8508298 -8.85082597 -8.85084776 -8.85080847 -8.85083094
-8.85075413 -8.85081273 -8.8507709 -8.85077429]
Variational energy of final HF state: -8.850853114414434
See the examples in Running SAFIRE for how to run AFQMC.