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Commit 06e234da authored by Johanna Zijderveld's avatar Johanna Zijderveld
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start working on a graphene hubbard tutorial

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---
jupytext:
text_representation:
extension: .md
format_name: myst
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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:
$$ Hubbardd $$
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