pymf

pymf is a Python package for numerical self-consistent mean-field calculations in tight-binding systems using Hartree-Fock approximation. Its interface is designed to allow users to control cost functions and numerical solvers. Additionally, it has an interface with Kwant for simple construction of tight-binding models.

Installation

pip install pymf

Usage

Finding a mean-field groundstate Hamiltonian is a 4-step process. We exemplify with the one-dimensional Hubbard model with two atoms per unit cell.

1. Define the non-interacting and interacting part of the Hamiltonian separately as hopping dictionaries.

# Hopping matrix
hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))
# Non-interacting Hamiltonian
h_0 = {(0,): hopp + hopp.T.conj(), (1,): hopp, (-1,): hopp.T.conj()}
# Interacting Hamiltonian
U=2
s_x = np.array([[0, 1], [1, 0]])
h_int = {(0,): U * np.kron(np.eye(2), s_x),}

2. Import pymf and combine the non-interacting and interacting Hamiltonians into a Model object.

# Number of electrons per unit cell
filling = 2
# Define model
model = pymf.Model(h_0, h_int, filling)

3. Provide a starting guess and the number of k-points to use the solver function and find the mean-field Hamiltonian.

# Generate a random guess
guess = pymf.generate_guess(frozenset(h_int), ndof=4)
# Compute groundstate Hamiltonian
mf_sol = pymf.solver(model, guess, nk=nk)

4. Add the mean-field correction to the non-interacting part to calculate the total Hamiltonian.

h_mf = pymf.add_tb(h_0, mf_sol)

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