Tutorials Overview

LatticeQM provides a sequence of Jupyter notebooks in extra/tutorial/ that walk through progressively more advanced workflows. Each documentation page in this section mirrors a notebook, highlighting the learning goals, main API calls, and checkpoints to verify that results look sensible.

Running the notebooks

Launch Julia in the project environment:

julia --project=.
using Pkg; Pkg.instantiate()

Start Jupyter (or VS Code) with the instantiated environment:
```
using IJulia; notebook(dir="extra/tutorial")
```
Execute cells in order. When a tutorial saves artefacts (plots, HDF5 files, logs), they appear alongside the notebook or within its output/ subfolder.

If you prefer a headless run to validate the notebooks, you can automate notebook execution with a simple Julia script and review the generated artefacts.

Tutorial roadmap

#	Topic	Notebook	Highlights	Notes
1	Structure & Geometry	`Tutorial1_Structure.ipynb`	Build lattices from scratch, explore predefined geometries, render 2D layouts.	Establishes terminology used throughout the docs.
2	Band Structures	`Tutorial2_Bands.ipynb`	Construct graphene Hamiltonians, sample Brillouin-zone paths, plot band dispersions.	Reuses geometries from Tutorial 1.
3	Haldane Model & Topology	`Tutorial3_Haldane.ipynb`	Add topological mass terms, compute Chern numbers, visualise edge modes.	Introduces topology utilities.
4	Twisted Bilayer Graphene	`Tutorial4_Twisted.ipynb`	Build large moiré lattices, compare continuum and lattice approaches, manage memory footprint.	`Tutorial4_Twisted2/3` capture experimental variations—treat their outputs as provisional until revalidated.
5	Hofstadter Butterfly	`Tutorial5_Hofstadter.ipynb`	Thread magnetic flux, generate Hofstadter spectra, analyse fractal band structures.	Heavy k-point sampling; expect longer runtimes.
6	Mean-field Self-Consistency	`Tutorial6_Meanfield.ipynb`	Run Hartree–Fock loops, inspect convergence metrics, export density matrices.	Shares utilities with `extra/examples/graphene/hubbardmeanfield_*`.
7	Floquet Dynamics	`Tutorial7_Floquet.ipynb`	Construct time-periodic drives, compute quasienergy spectra, monitor resonances.	Builds on modules co-authored with Tobias Kästli.
8	Superconductivity (BdG)	`Tutorial8_Superconductivity.ipynb`	Build Bogoliubov–de Gennes Hamiltonians, solve mean-field pairing self-consistently, inspect Nambu spectra.	Reuses the Hartree–Fock infrastructure from Tutorial 6.

For background reading and additional implementation details, cross-reference the Concept Guides and the repository examples under extra/examples/.