README.md

pymf

What is pymf?

pymf is a Python package that performs self-consistent mean-field calculations on tight-binding models. It aims to solve the following interacting many-body Hamiltonians:

\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,

by finding 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.

• Sufficiently time-effective

  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

We provide pymf as a free software under BSD license. If you have used pymf for work that has lead to a scientific publication, please mention the fact that you used it explicitly in the text body. For example, you may add

the numerical calculations were performed using the pymf code

to the description of your numerical calculations. In addition, we ask you to cite the Zenodo repository:

zenodo red here