README.md

pymf

What is pymf?

pymf is a Python package that performs self-consistent Hartree-Fock calculations on tight-binding models. It aims to find the groundstate of a Hamiltonian with density-density interactions

\hat{H} = \hat{H_0} + \hat{V} = \sum_{ij} h_{ij} c^\dagger_{i} c_{j} + \frac{1}{2} \sum_{ij} v_{ij} \hat{n}_i \hat{n}_j,

and computes the mean-field correction \hat{V}_{\text{MF}} which approximates the interaction term:

\hat{V} \approx \hat{V}_{\text{MF}} = \sum_{ij} \tilde{v}_{ij} c^\dagger_{i} c_{j}.

For more details, refer to the theory overview and algorithm description.

How to use pymf?

The calculation of a mean-field Hamiltonian is a simple 3-step process:

1. Define

   To specify the interacting problem, use a Model object which collects:

   • Non-interacting Hamiltonian as a tight-binding dictionary.
   • Interaction Hamiltonian as a tight-binding dictionary.
   • Particle filling number in the unit cell.

2. Guess

   Construct a starting guess for the mean-field correction.

3. Solve

   Solve for the mean-field correction using the solver function and add it to the non-interacting part to obtain the total mean-field Hamiltonian.

import pymf

#Define
h_0 = {(0,) : onsite, (1,) : hopping, (-1,) : hopping.T.conj()}
h_int = {(0,) : onsite_interaction}
model = pymf.Model(h_0, h_int, filling=2)

#Guess
guess = pymf.generate_guess(guess_hopping_keys, ndof)

#Solve
mf_correction = pymf.solver(model, guess)
h_mf = pymf.add_tb(h_0, mf_correction)

For more details and examples on how to use the package, we refer to the tutorials.

Why pymf?

Here is why you should use pymf:

• Simple

  The workflow is straightforward. Interface with Kwant allows easy creation of complicated tight-binding systems and interactions.

• Extensible

  pymf's code is structured to be easy to understand, modify and extend.

• Optimized numerical workflow

  Introduces minimal overhead to the calculation of the mean-field Hamiltonian.

What pymf doesn't do (yet)

Here are some features that are not yet implemented but are planned for future releases:

• Superconductive order parameters. Mean-field Hamiltonians do not include pairing terms.
• General interactions. We allow only density-density interactions (e.g. Coulomb) which can be described by a second-order tensor.
• Temperature effects. Density matrix calculations are done at zero temperature.

Installation

pip install pymf

Citing pymf

If you have used pymf for work that has lead to a scientific publication, please cite us as:

@misc{pymf,
  author = {Vilkelis, Kostas and Zijderveld,  R. Johanna and Akhmerov, Anton R. and Manesco, Antonio L.R.},
  doi = {10.5281/zenodo.11149850},
  month = {5},
  title = {pymf},
  year = {2024}
}