Combine with draft for `index.md`

README.md

@@ -10,10 +10,9 @@ pip install pymf
 
 ## Usage
 
-The algorithm consists of a few simple steps. We exemplify with the one-dimensional Hubbard model with two atoms per unit cell.
-
-1. Define the Hamiltonian
+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.
 ```python
 # Hopping matrix
 hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))
@@ -24,23 +23,23 @@ U=2
 s_x = np.array([[0, 1], [1, 0]])
 h_int = {(0,): U * np.kron(np.eye(2), s_x),}
 ```
-
-2. Combine non-interacting and interacting Hamiltonians into a model.
-
+2. Import `pymf` and combine the non-interacting and interacting Hamiltonians into a `Model` object.
 ```python
 # Number of electrons per unit cell
 filling = 2
 # Define model
 model = pymf.Model(h_0, h_int, filling)
 ```
-
-3. Compute the groundstate Hamiltonian.
-
+3. Provide a starting guess and the number of k-points to use the `solver` function and find the mean-field Hamiltonian.
 ```python
 # Generate a random guess
 guess = pymf.generate_guess(frozenset(h_int), ndof=4)
 # Compute groundstate Hamiltonian
-gs_hamiltonian = pymf.solver(model, guess, nk=nk)
+mf_sol = pymf.solver(model, guess, nk=nk)
+```
+4. Add the mean-field correction to the non-interacting part to calculate the total Hamiltonian.
+```python
+h_mf = pymf.add_tb(h_0, mf_sol)
 ```
 
 # Citing `pymf`