MeanFi

What is MeanFi?

MeanFi 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 MeanFi?

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 meanfi

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

#Guess
guess = meanfi.guess_tb(guess_hopping_keys, ndof)

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

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

Why MeanFi?

Here is why you should use MeanFi:

• Simple

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

• Extensible

  MeanFi'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 MeanFi 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 meanfi

Citing MeanFi

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

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