Examples

Everything related to constructing examples that motivate and teach how to use our package. This includes:

• coming up with new interesting physical systems
• cleaning up the existing ones

and likely more.

docs/source/graphene_example.md

+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.14.4
+kernelspec:
+  display_name: Python 3 (ipykernel)
+  language: python
+  name: python3
+---
+
+# Graphene and extended Hubbard
+
+## The physics
+
+This tutorial serves as a simple example of using the meanfield algorithm in two dimensions in combination with using Kwant. We will consider a simple tight-binding model of graphene with a Hubbard interaction. The graphene system is first created using Kwant. For the basics of creating graphene with Kwant we refer to [this](https://kwant-project.org/doc/1/tutorial/graphene) tutorial.
+
+We begin with the basic imports
+
+```{code-cell} ipython3
+import numpy as np
+import matplotlib.pyplot as plt
+from codes imort model, solvers, kwant_examples, kwant_helper, tb
+```
+
+##  Preparing the model
+
+We first translate this model from a Kwant system to a tight-binding dictionary. In the tight-binding dictionary the keys denote the hoppings while the values are the hopping amplitudes. 
+
+```{code-cell} ipython3
+# Create translationally-invariant `kwant.Builder`
+graphene_builder, int_builder = kwant_examples.graphene_extended_hubbard()
+h_0 = kwant_utils.builder_to_tb(graphene_builder)
+```
+
+We also use Kwant to create the Hubbard interaction. The interaction terms are  described by: 
+
+$$ Hubbardd $$