A minimal ALF run - ALF Tutorial

In this bare-bones example we use the pyALF interface to run the canonical Hubbard model on a default configuration: a $6\times6$ square grid, with interaction strength $U=4$ and inverse temperature $\beta = 5$ .

Bellow we go through the steps for performing the simulation and outputting observables.

1. Import ALF_source and Simulation classes from the py_alf python module, which provide the interface with ALF:

from py_alf import ALF_source, Simulation  # Interface with ALF

2. Create an instance of ALF_source, downloading the ALF source code from the ALF repository, if alf_dir does not exist. Gets alf_dir from environment variable $ALF_DIR, or defaults to “./ALF”, if not present:

alf_src = ALF_source(branch='master')

3. Create an instance of Simulation, overwriting default parameters as desired:

sim = Simulation(
    alf_src,
    "Hubbard",                    # Name of Hamiltonian
    {                             # Dictionary overwriting default parameters
        "Lattice_type": "Square"
    },
    machine='GNU'  # Change to "intel", or "PGI" if gfortran is not installed
)

4. Compile ALF. The first time it will also download and compile HDF5, which could take $\sim15$ minutes.

sim.compile()

Compiling ALF... 
Cleaning up Prog/
Cleaning up Libraries/
Cleaning up Analysis/
Compiling Libraries

entanglement_mod.F90:35:2:

   35 | #warning "You are compiling entanglement without MPI. No results possible"
      |  1~~~~~~
Warning: #warning "You are compiling entanglement without MPI. No results possible" [-Wcpp]
ar: creating modules_90.a
ar: creating libqrref.a

Compiling Analysis
Compiling Program
Parsing Hamiltonian parameters
filename: Hamiltonians/Hamiltonian_Kondo_smod.F90
filename: Hamiltonians/Hamiltonian_Hubbard_smod.F90
filename: Hamiltonians/Hamiltonian_Hubbard_Plain_Vanilla_smod.F90
filename: Hamiltonians/Hamiltonian_tV_smod.F90
filename: Hamiltonians/Hamiltonian_LRC_smod.F90
filename: Hamiltonians/Hamiltonian_Z2_Matter_smod.F90
Compiling program modules
Link program
Done.

5. Perform the simulation as specified in sim:

sim.run()

Prepare directory "/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square" for Monte Carlo run.
Create new directory.
Run /home/jonas/Programs/ALF/Prog/ALF.out
 ALF Copyright (C) 2016 - 2021 The ALF project contributors
 This Program comes with ABSOLUTELY NO WARRANTY; for details see license.GPL
 This is free software, and you are welcome to redistribute it under certain conditions.
 No initial configuration

6. Perform some simple analysis:

sim.analysis()

### Analyzing /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square ###
/home/jonas/Programs/pyALF/Notebooks
Scalar observables:
Ener_scal
Kin_scal
Part_scal
Pot_scal
Histogram observables:
Equal time observables:
Den_eq
Green_eq
SpinT_eq
SpinXY_eq
SpinZ_eq
Time displaced observables:
Den_tau
Green_tau
SpinT_tau
SpinXY_tau
SpinZ_tau

7. Read analysis results into a Pandas Dataframe with one row per simulation, containing parameters and observables:

obs = sim.get_obs()

obs

$\bullet$ The internal energy of the system (and its error) are accessed by:

obs.iloc[0][['Ener_scal0', 'Ener_scal0_err', 'Ener_scal_sign', 'Ener_scal_sign_err']]

$\bullet$ The simulation can be resumed by calling sim.run() again, increasing the precision of results:

sim.run()
sim.analysis()
obs2 = sim.get_obs()
obs2.iloc[0][['Ener_scal0', 'Ener_scal0_err', 'Ener_scal_sign', 'Ener_scal_sign_err']]

Prepare directory "/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square" for Monte Carlo run.
Resuming previous run.
Run /home/jonas/Programs/ALF/Prog/ALF.out
 ALF Copyright (C) 2016 - 2021 The ALF project contributors
 This Program comes with ABSOLUTELY NO WARRANTY; for details see license.GPL
 This is free software, and you are welcome to redistribute it under certain conditions.
### Analyzing /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square ###
/home/jonas/Programs/pyALF/Notebooks
Scalar observables:
Ener_scal
Kin_scal
Part_scal
Pot_scal
Histogram observables:
Equal time observables:
Den_eq
Green_eq
SpinT_eq
SpinXY_eq
SpinZ_eq
Time displaced observables:
Den_tau
Green_tau
SpinT_tau
SpinXY_tau
SpinZ_tau
/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square
No orbital locations saved.

Ener_scal0           -29.609245
Ener_scal0_err         0.136803
Ener_scal_sign              1.0
Ener_scal_sign_err          0.0
Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object

print("\nRunning again reduced the error from\n",
      obs.iloc[0][['Ener_scal0_err']], "\nto\n",
      obs2.iloc[0][['Ener_scal0_err']])


Running again reduced the error from
 Ener_scal0_err    0.13032
Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object 
to
 Ener_scal0_err    0.136803
Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object

Note: To run a fresh simulation - instead of performing a refinement over previous run(s) - the Monte Carlo run directory should be deleted before rerunning.

3.1Exercises¶

Check info/help commands such as help(alf_src), alf_src.get_ham_names(), and alf_src.get_default_params('Hubbard').
Rerun once again and check the new improvement in precision.
Look at a few other observables (sim.analysis() outputs the names of those available).
Change the lattice size by adding, e.g., \"L1\": 4, and \"L2\": 1, to the simulation parameters definitions of sim (step 2).

3 A minimal ALF run

3.1Exercises¶