MeanFi

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:

\[ \hat{V} \approx \hat{V}^{\text{MF}} =\sum_{ij} \tilde{v}_{ij} c_{i}^{\dagger} c_{j}. \]

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:

  • Superconducting 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 rank two 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}
}
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