diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml
new file mode 100644
index 0000000..5e7c523
--- /dev/null
+++ b/.github/workflows/deploy.yml
@@ -0,0 +1,59 @@
+name: Jupyter Book (via myst) GitHub Pages Deploy
+on:
+  push:
+    branches: ['**']
+env:
+  BASE_URL: /${{ github.event.repository.name }}
+
+permissions:
+  contents: read
+  pages: write
+  id-token: write
+
+concurrency:
+  group: 'pages-${{ github.ref }}'
+  cancel-in-progress: true
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v6
+      - uses: actions/setup-node@v6
+        with:
+          node-version: 24.x
+      - name: Install Jupyter Book (via myst)
+        run: npm install -g jupyter-book
+      - name: Build HTML Assets
+        working-directory: jupyterbook
+        run: jupyter-book build --html
+      - name: Upload Jupyter Book HTML artifact
+        uses: actions/upload-artifact@v6
+        with:
+          name: jupyter-book-html
+          path: jupyterbook/_build/html
+          if-no-files-found: error
+
+  deploy_pages:
+    name: Deploy GitHub Pages (main only)
+    runs-on: ubuntu-slim
+    needs: [build]
+    if: github.ref == 'refs/heads/main'
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    steps:
+      - name: Download Jupyter Book HTML
+        uses: actions/download-artifact@v7
+        with:
+          name: jupyter-book-html
+          path: public
+      - name: Configure Pages
+        uses: actions/configure-pages@v5
+      - name: Upload Pages artifact
+        uses: actions/upload-pages-artifact@v4
+        with:
+          path: public
+      - name: Deploy to Pages
+        id: deployment
+        uses: actions/deploy-pages@v4
diff --git a/jupyterbook/.gitignore b/jupyterbook/.gitignore
new file mode 100644
index 0000000..eac0968
--- /dev/null
+++ b/jupyterbook/.gitignore
@@ -0,0 +1,2 @@
+# MyST build outputs
+_build
diff --git a/jupyterbook/myst.yml b/jupyterbook/myst.yml
new file mode 100644
index 0000000..19639b7
--- /dev/null
+++ b/jupyterbook/myst.yml
@@ -0,0 +1,34 @@
+# See docs at: https://mystmd.org/guide/frontmatter
+version: 1
+project:
+  numbering:
+    title: true
+    headings: true
+  id: 72d8ee77-e3e8-443f-a297-3a1131f0bb48
+  title: ALF Tutorial (draft)
+  description: A tutorial for the ALF project
+  # keywords: []
+  # authors: []
+  github: https://github.com/ALF-QMC/ALF_Tutorial
+  toc:
+    # Auto-generated by `myst init --write-toc`
+    - file: source/01-intro.md
+    - file: source/02-installation.md
+    - file: source/03-minimal_ALF_run.ipynb
+    - file: source/04-nice-physics.md
+      children:
+      - file: source/04-nice-physics/bec.ipynb
+    - file: source/05-caveats.md
+      children:
+      - file: source/05-caveats/warmup.ipynb
+      - file: source/05-caveats/autocorrelation.ipynb
+      - file: source/05-caveats/delta-tau.ipynb
+      - file: source/05-caveats/finite-size-effects.ipynb
+
+    - file: source/06-fortran.md
+
+site:
+  template: book-theme
+  options:
+  #   favicon: favicon.ico
+  #   logo: site_logo.png
diff --git a/jupyterbook/pyproject.toml b/jupyterbook/pyproject.toml
new file mode 100644
index 0000000..39c8d00
--- /dev/null
+++ b/jupyterbook/pyproject.toml
@@ -0,0 +1,7 @@
+[project]
+name = "jupyterbook"
+version = "0.1.0"
+requires-python = ">=3.14"
+dependencies = [
+    "jupyter-book>=2.1.6",
+]
diff --git a/jupyterbook/source/01-intro.md b/jupyterbook/source/01-intro.md
new file mode 100644
index 0000000..326514f
--- /dev/null
+++ b/jupyterbook/source/01-intro.md
@@ -0,0 +1,19 @@
+# ALF Tutorial (work in progress)
+
+:::{attention} Work in progress
+This is an unfinished draft of a new version of the tutorial based on [Jupyter Book](https://jupyterbook.org).
+:::
+
+This is a tutorial for using [ALF](https://github.com/ALF-QMC/ALF/) and [pyALF](https://github.com/ALF-QMC/pyALF/) intended to get you started from zero up to your own first projects.
+
+Up until [Sec. 6](06-fortran.md), the documents revolves around [Jupyter Notebooks](https://jupyter.org/) that can be downloaded to run locally. They are interactive documents that combine code, narration and display of data in one file.
+
+
+## Outline of this document
+
+2. [](02-installation.md): Brief instructions to set up the prerequisites for this tutorial. For more details, see the documentation of [ALF](https://alf.physik.uni-wuerzburg.de/doc.pdf) and [pyALF](https://alf.physik.uni-wuerzburg.de/pyalf-doc/source/installation.html)
+3. [](03-minimal_ALF_run.ipynb): A simple example running ALF via pyALF. This is a [Jupyter Notebook](https://jupyter.org/) that can be downloaded to run locally.
+4. [](04-nice-physics.md): A few Jupyter Notebooks that display (py)ALF's capabilities by reproducing nice physics phenomena.
+5. [](05-caveats.md): A few Jupyter Notebooks that demonstrate common caveats and how to handle them.
+6. [](06-fortran.md): Here, we go beyond Jupyter Notebooks and write Fortran code to modify existing ALF Hamiltonians.
+
diff --git a/jupyterbook/source/02-installation.md b/jupyterbook/source/02-installation.md
new file mode 100644
index 0000000..c5a4cc3
--- /dev/null
+++ b/jupyterbook/source/02-installation.md
@@ -0,0 +1,40 @@
+# Installation
+ALF is pretty self-contained, you only need a LAPACK and a BLAS implementation as external libraries. For compiling the source code you need make and a Fortran 2003 compatible Compiler.
+
+pyALF, the Python interface for ALF, also demands only Python, Jupiter and a few basic Python packages: SciPy, NumPy and matplotlib.
+
+## Dependencies
+
+### Python
+
+If you do not yet have a Python environment with working pip, we recommend [miniforge](https://github.com/conda-forge/miniforge).
+
+The necessary Python packages can be easily installed on a variety of platforms — all that is needed is to issue the command:
+```bash
+conda install  ipython jupyterlab scipy numpy matplotlib
+```
+Miniforge is recommended due to its convenience, but the system's package management (e.g., apt-get) or Python's own package management, pip3, can be used instead if preferred.
+
+### ALF packages
+
+* **Linux**   
+  To install the relevant ALF packages.
+  - **Debian/Ubuntu/Linux Mint**:  `sudo apt-get install gfortran liblapack-dev make`
+  - **Red Hat/Fedora/CentOS**:  `sudo dnf install gcc-gfortran make liblapack-devel`
+  - **OpenSuSE/SLES**:  `sudo zypper install gcc-gfortran make lapack-devel`
+  - **Arch Linux**:  `pacman -S make gcc-fortran lapack`
+
+* **Other Unixes**   
+  gfortran and the lapack implementation from netlib.org should be available for your system. Consult the documentation of your system on how to install the relevant packages. The package names from linux should give good starting points for your search.
+
+* **MacOS**   
+  gfortran for MacOS can be found at https://gcc.gnu.org/wiki/GFortranBinaries#MacOS. Detailed information on how to install the package  can be found at: https://gcc.gnu.org/wiki/GFortranBinariesMacOS. You will need to have Xcode as well as the  Apple developer tools installed. 
+
+* **Windows**   
+  For Windows, we recommend using the Windows Subsystem for Linux, which can be installed following this guide https://learn.microsoft.com/en-us/windows/wsl/install and then proceed accoring to the instructions for Linux.
+
+## Building
+After you have obtained the source code of [ALF](https://git.physik.uni-wuerzburg.de/ALF/ALF/) and [pyALF](https://git.physik.uni-wuerzburg.de/ALF/pyALF/), and have set up the build environment, you need to build the source files. Executing `make` in the ALF's root directory does the job, and you can check the tutorial for more details.
+
+## Editors
+For the coding parts of the exercises we recommend to use a text editor. Linux usually have one installed like kwrite, kate or gedit(emacs and VI work great, too) and for the Windows users we recommend Notepad++. Jupyter notebooks of course can be edited in a browser.
diff --git a/jupyterbook/source/03-minimal_ALF_run.ipynb b/jupyterbook/source/03-minimal_ALF_run.ipynb
new file mode 100644
index 0000000..18c17d7
--- /dev/null
+++ b/jupyterbook/source/03-minimal_ALF_run.ipynb
@@ -0,0 +1,559 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "(minimal-run)=\n",
+    "# A minimal ALF run"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this bare-bones example we use the [pyALF](https://github.com/ALF-QMC/pyALF) interface to run the canonical Hubbard model on a default configuration: a $6\\times6$ square grid, with interaction strength $U=4$ and inverse temperature $\\beta = 5$.  \n",
+    "\n",
+    "Bellow we go through the steps for performing the simulation and outputting observables.\n",
+    "\n",
+    "---\n",
+    "\n",
+    "**1.** Import `ALF_source` and `Simulation` classes from the `py_alf` python module, which provide the interface with ALF:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from py_alf import ALF_source, Simulation  # Interface with ALF"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**2.** Create an instance of `ALF_source`, downloading the ALF source code from the [ALF repository](https://github.com/ALF-QMC/ALF/-/tree/master/), if `alf_dir` does not exist. Gets alf_dir from environment variable `$ALF_DIR`, or defaults to \"./ALF\", if not present:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Checking out branch master\n",
+      "Your branch is up to date with 'origin/master'.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Switched to branch 'master'\n"
+     ]
+    }
+   ],
+   "source": [
+    "alf_src = ALF_source(branch='master')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**3.** Create an instance of `Simulation`, overwriting default parameters as desired:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sim = Simulation(\n",
+    "    alf_src,\n",
+    "    \"Hubbard\",                    # Name of Hamiltonian\n",
+    "    {                             # Dictionary overwriting default parameters\n",
+    "        \"Lattice_type\": \"Square\"\n",
+    "    },\n",
+    "    machine='GNU'  # Change to \"intel\", or \"PGI\" if gfortran is not installed\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**4.** Compile ALF. The first time it will also download and compile HDF5, which could take $\\sim15$ minutes."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "scrolled": true,
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Compiling ALF... \n",
+      "Cleaning up Prog/\n",
+      "Cleaning up Libraries/\n",
+      "Cleaning up Analysis/\n",
+      "Compiling Libraries\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "entanglement_mod.F90:35:2:\n",
+      "\n",
+      "   35 | #warning \"You are compiling entanglement without MPI. No results possible\"\n",
+      "      |  1~~~~~~\n",
+      "Warning: #warning \"You are compiling entanglement without MPI. No results possible\" [-Wcpp]\n",
+      "ar: creating modules_90.a\n",
+      "ar: creating libqrref.a\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Compiling Analysis\n",
+      "Compiling Program\n",
+      "Parsing Hamiltonian parameters\n",
+      "filename: Hamiltonians/Hamiltonian_Kondo_smod.F90\n",
+      "filename: Hamiltonians/Hamiltonian_Hubbard_smod.F90\n",
+      "filename: Hamiltonians/Hamiltonian_Hubbard_Plain_Vanilla_smod.F90\n",
+      "filename: Hamiltonians/Hamiltonian_tV_smod.F90\n",
+      "filename: Hamiltonians/Hamiltonian_LRC_smod.F90\n",
+      "filename: Hamiltonians/Hamiltonian_Z2_Matter_smod.F90\n",
+      "Compiling program modules\n",
+      "Link program\n",
+      "Done.\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim.compile()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**5.** Perform the simulation as specified in `sim`:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prepare directory \"/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square\" for Monte Carlo run.\n",
+      "Create new directory.\n",
+      "Run /home/jonas/Programs/ALF/Prog/ALF.out\n",
+      " ALF Copyright (C) 2016 - 2021 The ALF project contributors\n",
+      " This Program comes with ABSOLUTELY NO WARRANTY; for details see license.GPL\n",
+      " This is free software, and you are welcome to redistribute it under certain conditions.\n",
+      " No initial configuration\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim.run()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**6.** Perform some simple analysis:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "### Analyzing /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square ###\n",
+      "/home/jonas/Programs/pyALF/Notebooks\n",
+      "Scalar observables:\n",
+      "Ener_scal\n",
+      "Kin_scal\n",
+      "Part_scal\n",
+      "Pot_scal\n",
+      "Histogram observables:\n",
+      "Equal time observables:\n",
+      "Den_eq\n",
+      "Green_eq\n",
+      "SpinT_eq\n",
+      "SpinXY_eq\n",
+      "SpinZ_eq\n",
+      "Time displaced observables:\n",
+      "Den_tau\n",
+      "Green_tau\n",
+      "SpinT_tau\n",
+      "SpinXY_tau\n",
+      "SpinZ_tau\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim.analysis()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**7.** Read analysis results into a Pandas Dataframe with one row per simulation, containing parameters and observables:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square\n",
+      "No orbital locations saved.\n"
+     ]
+    }
+   ],
+   "source": [
+    "obs = sim.get_obs()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>continuous</th>\n",
+       "      <th>ham_chem</th>\n",
+       "      <th>ham_t</th>\n",
+       "      <th>ham_t2</th>\n",
+       "      <th>ham_tperp</th>\n",
+       "      <th>ham_u</th>\n",
+       "      <th>ham_u2</th>\n",
+       "      <th>mz</th>\n",
+       "      <th>l1</th>\n",
+       "      <th>l2</th>\n",
+       "      <th>...</th>\n",
+       "      <th>SpinXY_tauK_err</th>\n",
+       "      <th>SpinXY_tauR</th>\n",
+       "      <th>SpinXY_tauR_err</th>\n",
+       "      <th>SpinXY_tau_lattice</th>\n",
+       "      <th>SpinZ_tauK</th>\n",
+       "      <th>SpinZ_tauK_err</th>\n",
+       "      <th>SpinZ_tauR</th>\n",
+       "      <th>SpinZ_tauR_err</th>\n",
+       "      <th>SpinZ_tau_lattice</th>\n",
+       "      <th>lattice</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square</th>\n",
+       "      <td>0</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>1.0</td>\n",
+       "      <td>4.0</td>\n",
+       "      <td>4.0</td>\n",
+       "      <td>1</td>\n",
+       "      <td>6</td>\n",
+       "      <td>6</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[[0.22628722504550844, 0.37685459854025805, 0....</td>\n",
+       "      <td>[[0.0575988003757706, -0.10378742200171556, 0....</td>\n",
+       "      <td>[[0.01248834666799511, 0.036871289378260834, 0...</td>\n",
+       "      <td>{'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'a1': [1....</td>\n",
+       "      <td>[[0.9040036362034092, 0.5628191896020613, 0.61...</td>\n",
+       "      <td>[[0.1494786750311893, 0.06006336638595281, 0.0...</td>\n",
+       "      <td>[[0.1013442053139478, -0.11445552391592478, 0....</td>\n",
+       "      <td>[[0.06273438448505823, 0.056390780430637014, 0...</td>\n",
+       "      <td>{'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'a1': [1....</td>\n",
+       "      <td>{'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'N_coord'...</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>1 rows × 111 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                                                    continuous  ham_chem  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...           0       0.0   \n",
+       "\n",
+       "                                                    ham_t  ham_t2  ham_tperp  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...    1.0     1.0        1.0   \n",
+       "\n",
+       "                                                    ham_u  ham_u2  mz  l1  l2  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...    4.0     4.0   1   6   6   \n",
+       "\n",
+       "                                                    ...  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  ...   \n",
+       "\n",
+       "                                                                                      SpinXY_tauK_err  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.22628722504550844, 0.37685459854025805, 0....   \n",
+       "\n",
+       "                                                                                          SpinXY_tauR  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.0575988003757706, -0.10378742200171556, 0....   \n",
+       "\n",
+       "                                                                                      SpinXY_tauR_err  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.01248834666799511, 0.036871289378260834, 0...   \n",
+       "\n",
+       "                                                                                   SpinXY_tau_lattice  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  {'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'a1': [1....   \n",
+       "\n",
+       "                                                                                           SpinZ_tauK  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.9040036362034092, 0.5628191896020613, 0.61...   \n",
+       "\n",
+       "                                                                                       SpinZ_tauK_err  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.1494786750311893, 0.06006336638595281, 0.0...   \n",
+       "\n",
+       "                                                                                           SpinZ_tauR  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.1013442053139478, -0.11445552391592478, 0....   \n",
+       "\n",
+       "                                                                                       SpinZ_tauR_err  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  [[0.06273438448505823, 0.056390780430637014, 0...   \n",
+       "\n",
+       "                                                                                    SpinZ_tau_lattice  \\\n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  {'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'a1': [1....   \n",
+       "\n",
+       "                                                                                              lattice  \n",
+       "/home/jonas/Programs/pyALF/Notebooks/ALF_data/H...  {'L1': [6.0, 0.0], 'L2': [0.0, 6.0], 'N_coord'...  \n",
+       "\n",
+       "[1 rows x 111 columns]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "obs"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\bullet$ The internal energy of the system (and its error) are accessed by:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Ener_scal0           -29.821914\n",
+       "Ener_scal0_err          0.13032\n",
+       "Ener_scal_sign              1.0\n",
+       "Ener_scal_sign_err          0.0\n",
+       "Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "obs.iloc[0][['Ener_scal0', 'Ener_scal0_err', 'Ener_scal_sign', 'Ener_scal_sign_err']]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\bullet$ The simulation can be resumed by calling `sim.run()` again, increasing the precision of results:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "scrolled": true,
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prepare directory \"/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square\" for Monte Carlo run.\n",
+      "Resuming previous run.\n",
+      "Run /home/jonas/Programs/ALF/Prog/ALF.out\n",
+      " ALF Copyright (C) 2016 - 2021 The ALF project contributors\n",
+      " This Program comes with ABSOLUTELY NO WARRANTY; for details see license.GPL\n",
+      " This is free software, and you are welcome to redistribute it under certain conditions.\n",
+      "### Analyzing /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square ###\n",
+      "/home/jonas/Programs/pyALF/Notebooks\n",
+      "Scalar observables:\n",
+      "Ener_scal\n",
+      "Kin_scal\n",
+      "Part_scal\n",
+      "Pot_scal\n",
+      "Histogram observables:\n",
+      "Equal time observables:\n",
+      "Den_eq\n",
+      "Green_eq\n",
+      "SpinT_eq\n",
+      "SpinXY_eq\n",
+      "SpinZ_eq\n",
+      "Time displaced observables:\n",
+      "Den_tau\n",
+      "Green_tau\n",
+      "SpinT_tau\n",
+      "SpinXY_tau\n",
+      "SpinZ_tau\n",
+      "/home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square\n",
+      "No orbital locations saved.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "Ener_scal0           -29.609245\n",
+       "Ener_scal0_err         0.136803\n",
+       "Ener_scal_sign              1.0\n",
+       "Ener_scal_sign_err          0.0\n",
+       "Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sim.run()\n",
+    "sim.analysis()\n",
+    "obs2 = sim.get_obs()\n",
+    "obs2.iloc[0][['Ener_scal0', 'Ener_scal0_err', 'Ener_scal_sign', 'Ener_scal_sign_err']]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Running again reduced the error from\n",
+      " Ener_scal0_err    0.13032\n",
+      "Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object \n",
+      "to\n",
+      " Ener_scal0_err    0.136803\n",
+      "Name: /home/jonas/Programs/pyALF/Notebooks/ALF_data/Hubbard_Square, dtype: object\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"\\nRunning again reduced the error from\\n\",\n",
+    "      obs.iloc[0][['Ener_scal0_err']], \"\\nto\\n\",\n",
+    "      obs2.iloc[0][['Ener_scal0_err']])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Note**: To run a fresh simulation - instead of performing a refinement over previous run(s) - the Monte Carlo run directory should be deleted before rerunning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## Exercises\n",
+    "1. Check info/help commands such as `help(alf_src)`, `alf_src.get_ham_names()`, and `alf_src.get_default_params('Hubbard')`.\n",
+    "2. Rerun once again and check the new improvement in precision.\n",
+    "3. Look at a few other observables (`sim.analysis()` outputs the names of those available).\n",
+    "4. Change the lattice size by adding, e.g., `\\\"L1\\\": 4,` and `\\\"L2\\\": 1,` to the simulation parameters definitions of `sim` (step 2)."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.6"
+  },
+  "widgets": {
+   "application/vnd.jupyter.widget-state+json": {
+    "state": {},
+    "version_major": 2,
+    "version_minor": 0
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/jupyterbook/source/04-nice-physics.md b/jupyterbook/source/04-nice-physics.md
new file mode 100644
index 0000000..a28dd3e
--- /dev/null
+++ b/jupyterbook/source/04-nice-physics.md
@@ -0,0 +1 @@
+# Reproducing some nice physics
\ No newline at end of file
diff --git a/jupyterbook/source/04-nice-physics/bec.ipynb b/jupyterbook/source/04-nice-physics/bec.ipynb
new file mode 100644
index 0000000..9af12a0
--- /dev/null
+++ b/jupyterbook/source/04-nice-physics/bec.ipynb
@@ -0,0 +1,19 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "428b9c10",
+   "metadata": {},
+   "source": [
+    "# Bose-Einstein Condensate"
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/jupyterbook/source/05-caveats.md b/jupyterbook/source/05-caveats.md
new file mode 100644
index 0000000..2a34ab2
--- /dev/null
+++ b/jupyterbook/source/05-caveats.md
@@ -0,0 +1 @@
+# Demonstration of common caveats when using ALF
\ No newline at end of file
diff --git a/jupyterbook/source/05-caveats/autocorrelation.ipynb b/jupyterbook/source/05-caveats/autocorrelation.ipynb
new file mode 100644
index 0000000..df8efbe
--- /dev/null
+++ b/jupyterbook/source/05-caveats/autocorrelation.ipynb
@@ -0,0 +1,25 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d6374947",
+   "metadata": {},
+   "source": [
+    "# Autocorrelation time"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd1369bb",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/jupyterbook/source/05-caveats/delta-tau.ipynb b/jupyterbook/source/05-caveats/delta-tau.ipynb
new file mode 100644
index 0000000..82209bb
--- /dev/null
+++ b/jupyterbook/source/05-caveats/delta-tau.ipynb
@@ -0,0 +1,25 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0347b6ad",
+   "metadata": {},
+   "source": [
+    "# Imaginary time discretization error"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d66918e7",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/jupyterbook/source/05-caveats/finite-size-effects.ipynb b/jupyterbook/source/05-caveats/finite-size-effects.ipynb
new file mode 100644
index 0000000..dfd85e8
--- /dev/null
+++ b/jupyterbook/source/05-caveats/finite-size-effects.ipynb
@@ -0,0 +1,25 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "2ccf87ab",
+   "metadata": {},
+   "source": [
+    "# Finite Size Effects"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "01874b49",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/jupyterbook/source/05-caveats/warmup.ipynb b/jupyterbook/source/05-caveats/warmup.ipynb
new file mode 100644
index 0000000..a10b268
--- /dev/null
+++ b/jupyterbook/source/05-caveats/warmup.ipynb
@@ -0,0 +1,25 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "6d03fccb",
+   "metadata": {},
+   "source": [
+    "# Warmup time"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24c296cb",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/jupyterbook/source/06-fortran.md b/jupyterbook/source/06-fortran.md
new file mode 100644
index 0000000..28ae66f
--- /dev/null
+++ b/jupyterbook/source/06-fortran.md
@@ -0,0 +1,308 @@
+# Getting your hands dirty: writing new Fortran code
+
+This second part of the tutorial consists in a set of guided exercises that exemplify how to make basic additions to the code, taking as starting point the template-like, relatively self-contained submodule `Hamiltonian_Hubbard_Plain_Vanilla_smod.F90`, which is also a good display of ALF's internal workings.
+
+These worked-out exercises, together with ALF's modularity, boosted by its Predefined Structures, should make getting your hands dirty less daunting than it may sound.
+
+## Downloading and using the code and tutorial
+
+One can use the ALF package downloaded automatically by the Python script in the first part of this tutorial, or manually, by typing
+
+```bash
+git clone https://git.physik.uni-wuerzburg.de/ALF/ALF.git
+```
+
+in a shell. Similarly, to download the tutorial, including solutions, enter:
+
+```bash
+git clone https://git.physik.uni-wuerzburg.de/ALF/ALF_Tutorial.git
+```
+
+This document is found in the directory `Tutorial-ALF-{tutALFver}`.
+
+The necessary environment variables and the directives for compiling the code are set by the script `configure.sh`:
+
+```bash
+source configure.sh GNU noMPI
+```
+
+followed by the command `make`. Details and further options are described in the package's documentation found in its repository.
+
+A workflow you can adopt for solving the exercises — or indeed using ALF in general — is the following:
+
+1. Compile the modified Hamiltonian module, for instance:  
+   `make all`
+2. Create a data directory with the content of `Start`:  
+   `cp -r ./Scripts_and_Parameters_files/Start ./Run  &&  cd ./Run/`
+3. Run its executable, e.g., serially:  
+   `$ALF_DIR/Prog/ALF.out`
+4. Perform default analyses[^analysis_sh]:  
+   `$ALF_DIR/Analysis/ana.out *`
+
+[^analysis_sh]: The `analysis.sh` bash script from earlier versions of ALF, run without arguments, is still available in the `Start` directory.
+
+The structure of the data files and details on the analysis output can be found in ALF's documentation.
+
+<!-- Two common pitfalls are:
+- forgetting to run `configure.sh`, and
+- not using different `Run` data directories for independent runs.
+-->
+
+### Exercise: Dimensional crossover
+
+Here we will modify the code so as to allow for different hopping matrix elements along the $x$ and $y$ directions of a square lattice.
+
+#### Modifying the hopping
+
+To do so we start from the submodule `Hamiltonian_Hubbard_Plain_Vanilla_smod.F90`, which we here shorten to "`Vanilla`", found in `$ALF_DIR/Prog/Hamiltonians/`, proceeding as follows:
+
+- Add `Ham_Ty` to the `VAR_Hubbard_Plain_Vanilla` name space in the parameter file `parameters`.
+- Declare a new variable, `Ham_Ty`, in the module's specification on a new line between `!#PARAMETERS START# VAR_Hubbard_Plain_Vanilla` and the corresponding `!#PARAMETERS END#`.
+- Modify the hopping matrix in the subroutine `Ham_Hop` in `Vanilla`:
+
+```fortran
+Do I = 1,Latt%N
+   Ix = Latt%nnlist(I,1,0)
+   Op_T(1,nf)%O(I,  Ix) = cmplx(-Ham_T,    0.d0, kind(0.D0))
+   Op_T(1,nf)%O(Ix, I ) = cmplx(-Ham_T,    0.d0, kind(0.D0))
+   If ( L2 > 1 ) then
+      Iy = Latt%nnlist(I,0,1)
+!!!!!!! Modifications for Exercise 1a
+      !Op_T(1,nf)%O(I,  Iy) = cmplx(-Ham_T,    0.d0, kind(0.D0))
+      !Op_T(1,nf)%O(Iy, I ) = cmplx(-Ham_T,    0.d0, kind(0.D0))
+      Op_T(1,nf)%O(I,  Iy) = cmplx(-Ham_Ty,    0.d0, kind(0.D0))
+      Op_T(1,nf)%O(Iy, I ) = cmplx(-Ham_Ty,    0.d0, kind(0.D0))
+!!!!!!!
+   endif
+   Op_T(1,nf)%O(I,  I ) = cmplx(-Ham_chem, 0.d0, kind(0.D0))
+   Op_T(1,nf)%P(i) = i 
+Enddo
+```
+
+<!-- Note: If you'd like to run the simulation using MPI, you should also add the broadcasting call for `Ham_Ty` to `Ham_Set`. -->
+
+It is a good idea as well to get the new simulation parameter written into the file `info`, also a change in `Ham_Set`.
+
+In the directory `Solutions/Exercise_1` we have the modified and original submodules, as well as reference data and the necessary `Start` directory (remember to copy its contents to every new `Run` directory, and to have a different `Run` directory for each simulation).
+
+As an application of this code, we can once again consider a ladder system (e.g, a 2-leg ladder with `L1=14` and `L2=2`), for different values of `Ham_Ty`. The results you should obtain for the total spin correlation function (file `SpinT_eqJR`) are summarized in [](#fig-ladder).
+
+```{figure} Figures/ladder.pdf
+---
+width: 60%
+name: fig-ladder
+---
+Spin correlation functions along one leg for the Hubbard ladder. As $t_y$ grows the spin gap becomes large enough so as to detect the exponential decay of the spin correlation function on this small lattice size. The underlying physics of odd-even ladder systems is introduced in the article: Elbio Dagotto and T. M. Rice, "Surprises on the way from one- to two-dimensional quantum magnets: The ladder materials", Science **271**, 5249 (1996) pp. 618–623.
+```
+
+#### The SU(2) Hubbard-Stratonovich transformation
+
+The SU(2) Hubbard-Stratonovich decomposition couples to the density and conserves spin rotational symmetry. Introduce into the module `Hamiltonian_Hubbard_smod.F90` and into the name space `VAR_Hubbard` the same changes done to the `Vanilla` module, described in the previous item, and enter `Mz=.F.` in the `parameters` file (in order to choose the $SU(N)$ Hubbard interaction) and compare results to those of the $M_z$ decomposition above — especially with regard to numerical convergence.
+
+### Exercise: Defining a new model — The one-dimensional t-V model
+
+In this section, we will show what modifications have to be carried out for computing the physics of the one dimensional t-V model of spinless fermions.
+
+```{math}
+\hat{H} =  -t \sum_{i} \left( \hat{c}^{\dagger}_{i}  \hat{c}^{\phantom\dagger}_{i+a}      + \hat{c}^{\dagger}_{i+a}  \hat{c}^{\phantom\dagger}_{i} \right) - \frac{V}{2} \sum_{i}  \left( \hat{c}^{\dagger}_{i}  \hat{c}^{\phantom\dagger}_{i+a}      + \hat{c}^{\dagger}_{i+a}  \hat{c}^{\phantom\dagger}_{i} \right)^2 .
+```
+
+The above form is readily included in the ALF since the interaction is written in terms of a perfect square. Expanding the square yields (up to a constant) the desired model:
+
+```{math}
+\hat{H} =  -t \sum_{i} \left( \hat{c}^{\dagger}_{i}  \hat{c}^{\phantom\dagger}_{i+a}      + \hat{c}^{\dagger}_{i+a}  \hat{c}^{\phantom\dagger}_{i} \right)  + V  \sum_{i}  \left( \hat{n}_{i} - 1/2 \right)  \left( \hat{n}_{i+a} - 1/2 \right).
+```
+
+Note that the t-V model is already implemented in ALF in the module `Hamiltonian_tV_smod.F90` found in `$ALF_DIR/Prog/Hamiltonians/`. While it can be used for checking your own results[^tV_notebook], you are not supposed to reproduce that implementation — which is more general and makes use of predefined structures — but instead to write a simpler one, based on the module `Hamiltonian_Hubbard_Plain_Vanilla_smod.F90` as detailed below.
+
+[^tV_notebook]: A short simulation of the t-V model can be conveniently run using its Jupyter notebook available in pyALF.
+
+#### Define new model
+
+In the directory `Solutions/Exercise_2` we have duplicated the ALF and commented the changes that have to be carried out to the file `Hamiltonian_Hubbard_Plain_Vanilla_smod.F90`, which we here shorten to "`Vanilla`", found in `$ALF_DIR/Prog/Hamiltonians/`. The following are the essential steps to be carried out:
+
+- Add the `VAR_t_V` name space in the file `parameters` and set the necessary variables — or simply rename the `VAR_Hubbard_Plain_Vanilla` name space to `VAR_t_V` and, within it, `Ham_U` to `Ham_Vint`. (Ignore the name space `VAR_tV`, which is used by the general implementation mentioned above.)
+- Declare a new variable, `Ham_Vint`, in `Vanilla`'s specification.
+- Add the `VAR_t_V` name space (`namelist`) declaration at the `Ham_Set` subroutine of `Vanilla`, containing the same variables the name space contains in `parameters`, and read it in.
+- Still in the `Ham_set` subroutine of `Vanilla`: set `NF=1`, since we are working with spinless fermions; change the output to the info file.
+- In the `Ham_V` subroutine you have to add the new interaction. For a given bond at a given time slice, we need to decouple the interaction:
+
+```{math}
+e^{\Delta \tau \frac{V}{2} \left( \hat{c}^{\dagger}_{i}  \hat{c}^{\phantom\dagger}_{i+a}      + \hat{c}^{\dagger}_{i+a}  \hat{c}^{\phantom\dagger}_{i} \right)^2} = 
+\sum_{l= \pm1, \pm 2} \gamma_l e^{ \sqrt{\Delta \tau \frac{V}{2}}  \eta_l   \left( \hat{c}^{\dagger}_{i}  \hat{c}^{\phantom\dagger}_{i+a}      + \hat{c}^{\dagger}_{i+a}  \hat{c}^{\phantom\dagger}_{i} \right) } =  \sum_{l= \pm1, \pm 2} \gamma_l e^{ g  \eta_l   \left( \hat{c}^{\dagger}_{i},  \hat{c}^{\dagger}_{i+a}  \right)  O 
+    \left(\hat{c}^{\phantom\dagger}_{i},  \hat{c}^{\phantom\dagger}_{i+a} \right)^{T} }.
+```
+
+Here is how this translates in the code (the new integer variable, `i2`, should be declared):
+
+```fortran
+Allocate(Op_V(Ndim,N_FL))
+ do nf = 1,N_FL
+    do i  =  1, Ndim
+       call Op_make(Op_V(i,nf),2)
+    enddo
+ enddo
+ Do i = 1, Ndim  ! Runs over bonds = # of lattice sites in one-dimension. 
+    i2                = Latt%nnlist(i,1,0)
+    Op_V(i,nf)%P(1)   = i
+    Op_V(i,nf)%P(2)   = i2
+    Op_V(i,nf)%O(1,2) = cmplx(1.d0 ,0.d0, kind(0.d0))
+    Op_V(i,nf)%O(2,1) = cmplx(1.d0 ,0.d0, kind(0.d0)) 
+    Op_V(i,nf)%g      = sqrt(cmplx(Dtau*Ham_Vint/2.d0, 0.d0, kind(0.d0)))  
+    Op_V(i,nf)%alpha  = cmplx(0d0  ,0.d0, kind(0.d0))
+    Op_V(i,nf)%type   = 2
+    Call Op_set( Op_V(i,nf) )
+ enddo
+```
+
+- Finally, you have to update the `Obser` and `ObserT` routines for the calculation of equal- and time-displaced correlations. For the `t_V` model you can essentially use the same observables as for the `Hubbard_SU(2)` model in 1D — a step which requires a number of changes with respect to the `Vanilla` base, such as:
+
+```fortran
+!!!!! Modifications for Exercise 2
+ !Zpot = Zpot*ham_U                       ! Vanilla
+ Zpot = Zpot*Ham_Vint                     ! t-V
+ !!!!!
+```
+
+and
+
+```fortran
+!Zrho = Zrho + Grc(i,i,1) +  Grc(i,i,2)  ! Vanilla
+ Zrho = Zrho + Grc(i,i,1)                 ! t-V
+```
+
+with the observables being coded in the routine `Obser` as
+
+```fortran
+Z = cmplx(dble(N_SUN), 0.d0, kind(0.D0))
+ Do I1 = 1,Ndim
+    I = I1
+    no_I = 1
+    Do J1 = 1,Ndim
+       J = J1
+       no_J = 1
+       imj = latt%imj(I,J)
+       Obs_eq(1)%Obs_Latt(imj,1,no_I,no_J) =  Obs_eq(1)%Obs_Latt(imj,1,no_I,no_J) + &
+       &               Z * GRC(I1,J1,1) * ZP*ZS  ! Green
+       Obs_eq(2)%Obs_Latt(imj,1,no_I,no_J) =  Obs_eq(2)%Obs_Latt(imj,1,no_I,no_J) + &
+       &               Z * GRC(I1,J1,1) * GR(I1,J1,1) * ZP*ZS  ! SpinZ
+       Obs_eq(3)%Obs_Latt(imj,1,no_I,no_J) =  Obs_eq(3)%Obs_Latt(imj,1,no_I,no_J) + &
+       &               ( GRC(I1,I1,1) * GRC(J1,J1,1) * Z + &
+       &                 GRC(I1,J1,1) * GR(I1,J1,1 )       ) * Z * ZP*ZS  ! Den
+    enddo
+    Obs_eq(3)%Obs_Latt0(no_I) =  Obs_eq(3)%Obs_Latt0(no_I) + Z * GRC(I1,I1,1) * ZP * ZS
+ enddo
+```
+
+among other changes — with similar ones in the `ObserT` routine.
+
+All necessary changes are implemented and clearly indicated in the solution provided in `Solutions/Exercise_2/Hamiltonian_Hubbard_Plain_Vanilla_smod-Exercise_2.F90`.
+
+In the directory `Solutions/Exercise_2` we have the modified and original submodules, as well as reference data and the necessary `Start` directory (remember to copy its contents to every new `Run` directory, and to have a different `Run` directory for each simulation).
+
+#### Phase transition
+
+You can now run the code for various values of $V/t$. A Jordan-Wigner transformation will map the `t_V` model onto the XXZ chain:
+
+```{math}
+\hat{H} = J_{xx} \sum_{i}   \hat{S}^{x}_i \hat{S}^{x}_{i+a} +   \hat{S}^{y}_i \hat{S}^{y}_{i+a}  + J_{zz}  \sum_{i}\hat{S}^{z}_i \hat{S}^{z}_{i +a}\quad,
+```
+
+with $J_{zz} = V$ and $J_{xx} = 2t$. Hence, when $V/t = 2$ we reproduce the Heisenberg model. For $V/t > 2$ the model is in the Ising regime with long-range charge density wave order and is an insulator. In the regime $-2 < V/t < 2$ the model is metallic and corresponds to a Luttinger liquid. Finally, at $V/t < -2$ phase separation between hole rich and electron rich phases occur. [](#fig-tV) shows typical results for the density-density correlation function (file `Den_eqJR`).
+
+```{figure} Figures/tV.pdf
+---
+width: 60%
+name: fig-tV
+---
+Density-Density correlation functions of the t-V model. In the Luttinger liquid phase, $-2 < V/t < 2$, it is known that the density-density correlations decay as $\langle n(r) n(0)\rangle \propto \cos(\pi r) r^{-\left(1+K_\rho \right)}$ with $\left(1+K_\rho \right)^{-1}= \frac{1}{2} + \frac{1}{\pi} \arcsin \left( \frac{V}{2 |t|}\right)$ (A. Luther and I. Peschel, Calculation of critical exponents in two dimensions from quantum field theory in one dimension, Phys. Rev. B **12** (1975), pp. 3908–3917.) The interested reader can try to reproduce this result.
+```
+
+<!-- Challenge: How would you use the code to carry out simulations at $V/t < 0$? -->
+
+### Exercise: Adding a new observable
+
+This exercise illustrates the modifications that are required to implement a new observable, the correlation function of the bond-hopping in the 1-dimensional Hubbard chain. This observable is interesting in many different setups. For example, the model studied here exhibits an emergent $SO(4)$ symmetry that relates the anti-ferromagnetic order parameter and the bond dimerization (I. Affleck, PRL **55** (1985) pp. 1355; I. Affleck and F. D. M. Haldane, PRB **36** (1987) pp. 5291). Another example where this quantity is useful to investigate is the 1-dimensional Su-Schrieffer-Heeger model describing an electron-phonon system.
+
+#### Applying Wick's theorem
+
+Here the task is to define a new equal-time observable, the kinetic energy correlation, given by
+
+```{math}
+:label: eq-new-obs
+\left\langle \hat{O}_{i,\delta} \hat{O}_{j,\delta'} \right\rangle  -  \left\langle \hat{O}_{i,\delta} \right\rangle \left\langle \hat{O}_{j,\delta'} \right\rangle  =  S_O\big(i-j,\delta,\delta'\big)
+```
+
+where $i,j$ refer to the unit cells and $\delta$ encodes the bond label. Since we are working in 1D, there is only one bond per unit cell and $\delta=ax$ such that
+
+```{math}
+\hat{O}_{i,x} = \sum_{\sigma}\left( \hat{c}^\dagger_{i,\sigma}\hat{c}^{\phantom\dagger}_{i+ax,\sigma} +\mathrm{H.c.} \right).
+```
+
+Note that the first term of Eq. {eq}`eq-new-obs` is of the generic form $\sum_{\sigma,\sigma'}\left\langle \hat{c}^\dagger_{i_1,\sigma}\hat{c}^{\phantom\dagger}_{i_2,\sigma} \hat{c}^\dagger_{j_1,\sigma'}\hat{c}^{\phantom\dagger}_{j_2,\sigma'} \right\rangle$. This expectation value can be readily decomposed into single-particle Green functions by using Wick's theorem. It can be applied for a fixed field configuration $\Phi$ since the Hamiltonian $\hat{H}(\Phi)$ is then bi-linear in the fermion operators.
+
+```{math}
+\sum_{\sigma,\sigma'}\left\langle \hat{c}^\dagger_{i_1,\sigma}\hat{c}^{\phantom\dagger}_{i_2,\sigma} \hat{c}^\dagger_{j_1,\sigma'}\hat{c}^{\phantom\dagger}_{j_2,\sigma'} \right\rangle_\Phi = 
+\sum_{\sigma,\sigma'}\left(\left\langle \hat{c}^\dagger_{i_1,\sigma}\hat{c}^{\phantom\dagger}_{i_2,\sigma}\right\rangle_\Phi
+\left\langle\hat{c}^\dagger_{j_1,\sigma'}\hat{c}^{\phantom\dagger}_{j_2,\sigma'} \right\rangle_\Phi
++\left\langle \hat{c}^\dagger_{i_1,\sigma}\hat{c}^{\phantom\dagger}_{j_2,\sigma'}\right\rangle_\Phi
+\left\langle\hat{c}^{\phantom\dagger}_{i_2,\sigma}\hat{c}^\dagger_{j_1,\sigma'} \right\rangle_\Phi
+\right)
+```
+
+The second term vanishes for $\sigma\neq\sigma'$ due to flavor symmetry (Mz-decoupling used here in the vanilla version) or due to the $SU(2)$ symmetry (density decoupling available in the generic implementation of Hubbard model). The single-particle Green functions are provided in the `Obser` routine, where all equal-time observables are measured, as
+
+```{math}
+GRC(i,j,\sigma) & = \left\langle \hat{c}^\dagger_{i,\sigma}\hat{c}^{\phantom\dagger}_{j,\sigma}\right\rangle_\Phi\\
+GR(i,j,\sigma) & = \left\langle \hat{c}^{\phantom\dagger}_{i,\sigma}\hat{c}^\dagger_{j,\sigma}\right\rangle_\Phi .
+```
+
+#### Necessary code modifications
+
+In the directory `Solutions/Exercise_3` we have the modified and original submodule `Hamiltonian_Hubbard_Plain_Vanilla_smod.F90` found in `$ALF_DIR/Prog/Hamiltonians` (which we here shorten to "`Vanilla`"), as well as reference data and the necessary `Start` directory (remember to copy its contents to every new `Run` directory, and to have a different `Run` directory for each simulation). The following are the essential steps to be carried out:
+
+- Introduce the new observable and allocate the memory required to store the measurements. This is done in the subroutine `Alloc_obs(Ltau)` by increasing the length of the array `Obs_eq` appropriately and adding a new case to specify the filename in which the results are stored on disc. (You might want to revisit this section later on to add the time-displaced version of the correlation function by changing `Obs_tau` in the same fashion.)
+- The actual measurements are taken in the subroutine `Obser(GR,Phase,Ntau)`. While `GR` is passed to the subroutine, the first lines of code already implement the construct $\mathtt{GRC}=1-\mathtt{GR}^T$. (This section does not have to be modified, but it is useful to keep this in mind for future reference when you implement a new model from scratch.)
+- The measurement of an equal-time correlation function consists of two separate parts: the connected one given by the first term in Eq. {eq}`eq-new-obs`, and the background, given by the second term.
+- Implement the measurement of the connected part, stored as $\mathtt{Obs\_eq}(6)$ in this example, using the Wick decomposition sketched above.
+- Keep in mind that the background $\sum_i\left\langle \hat{O}_{i,\delta} \right\rangle\neq0$ is non-vanishing and has to be measured separately (you can compare with the density correlation function), and is stored in $\mathtt{Obs\_eq}(6)\%\mathtt{Obs\_Latt0}(1)$.
+- The analysis tool will then automatically combine both contributions and evaluate Eq. {eq}`eq-new-obs` using the jackknife method to estimate the mean and error of the correlation function.
+
+The 1-D Hubbard exhibits an emergent $SO(4)$ symmetry:
+
+```{math}
+\left\langle \bar{S}(r)S(0) \right\rangle  &\sim  \frac{(-1)^r}{r}\ln^d(r)\\
+\left\langle \hat{O}_{r,x} \hat{O}_{0,x} \right\rangle  -  \left\langle \hat{O}_{r,x} \right\rangle \left\langle \hat{O}_{0,x} \right\rangle  &\sim   \frac{(-1)^r}{r}\ln^\beta(r)
+```
+
+where $d=1/2$ and $\beta=-3/2$ (T. Sato, M. Hohenadler et al., Phys. Rev. B **104** (2021) L161105) and this exercise provides all the tools required to study it. Beware of the large system sizes, and therefore long run times, that are required to extract the logarithmic scaling corrections. More details are discussed in the appendix of above reference.
+
+Finally, it is straightforward to implement the time-displaced version of this correlation function, following essentially the same steps as described above. The observable is now stored in `Obs_tau`, the measurements are taken in `ObserT`, and you can find the implementation in the solution to this exercise as well.
+
+---
+
+## Appendix: Excluded exercise item from "Dimensional crossover"
+
+When running the code for the above ladder system and analyzing the spin correlation functions, `SpinZ_eqJR` and `SpinXY_eqJR` one will notice that it is hard to restore the SU(2) spin symmetry and that very long runs are required to obtain the desired equality
+
+```{math}
+\langle S^{z}_{i} S^{z}_{j}  \rangle  = \langle S^{y}_{i} S^{y}_{j}  \rangle  = \langle S^{x}_{i} S^{x}_{j}  \rangle. 
+```
+
+The structure of the output files `SpinZ_eqJR` and `SpinXY_eqJR` is described in the documentation. For the Mz Hubbard-Stratonovich transformation it is hence better to consider the improved estimator
+
+```{math}
+\langle \vec{S}_{i}  \cdot \vec{S}_{j}  \rangle
+```
+
+to compute the spin-spin correlations.
+
+Here the aim is to include the new equal-time observable $\langle \vec{S}_{i} \cdot \vec{S}_{j} \rangle$ in the `Hubbard_Mz` code. To achieve this, you will have to carry out the following steps.
+
+- In the subroutine `Alloc_obs` in the `Hamiltonian_example.f90` file you will have to add a new equal time observable with a call to `Call Obser_Latt_make(Obs_eq(I),Ns,Nt,No,Filename)` with `Ns = Latt%N; No = Norb; Filename ="SpinT", Nt=1, I=5`
+- In the subroutine `Obser` you will have to add the Wick decomposition of this observable.
+
+In the program `Hamiltonian_Examples.f90` to be found in the directory `Solutions/Exercise_2/Prog/` we have commented the changes that have to be carried out to add this observable. The new variable takes the name SpinT and the results you should obtain are summarized in [](#fig-ladder).
+
+
+
diff --git a/jupyterbook/source/Figures/Ener_B2.pdf b/jupyterbook/source/Figures/Ener_B2.pdf
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diff --git a/jupyterbook/source/Figures/ladder.pdf b/jupyterbook/source/Figures/ladder.pdf
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diff --git a/jupyterbook/source/Figures/ladder.plt b/jupyterbook/source/Figures/ladder.plt
new file mode 100644
index 0000000..42f7ea2
--- /dev/null
+++ b/jupyterbook/source/Figures/ladder.plt
@@ -0,0 +1,17 @@
+set terminal postscript eps enhanced solid color 'Times-Roman' 18
+set size 0.8,0.8
+set title "{L=14 Hubbard Ladder, {/Symbol b}t=10, U/t=4 }"
+set out 'ladder.eps'
+set fit errorvariables
+set xlabel "r"
+set ylabel "S(r,0)"
+
+plot "ladder.dat" i 0  u 1:2:3 w e lc rgb "black"      lt 1 pt 7 lw 2 t "t_y=0" ,  \
+      ''          i 0  u 1:2   w l lc rgb "black"      lt 1      lw 2 t "" ,       \
+      ''          i 1  u 1:2:3 w e lc rgb "red"        lt 1 pt 7 lw 2 t "t_y=1" ,  \
+      ''          i 1  u 1:2   w l lc rgb "red"        lt 1      lw 2 t "" ,       \
+      ''          i 2  u 1:2:3 w e lc rgb "royalblue"  lt 1 pt 7 lw 2 t "t_y=2" ,\
+      ''          i 2  u 1:2   w l lc rgb "royalblue"  lt 1      lw 2 t ""
+
+!epstopdf ladder.eps
+!evince ladder.pdf
diff --git a/jupyterbook/source/Figures/tV.pdf b/jupyterbook/source/Figures/tV.pdf
new file mode 100644
index 0000000..f3d0f76
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diff --git a/jupyterbook/source/Figures/tV.plt b/jupyterbook/source/Figures/tV.plt
new file mode 100644
index 0000000..6aac96b
--- /dev/null
+++ b/jupyterbook/source/Figures/tV.plt
@@ -0,0 +1,17 @@
+set terminal postscript eps enhanced solid color 'Times-Roman' 18
+set size 0.8,0.8
+set title "{L=28 tV model, {/Symbol b}t=20}"
+set out 'tV.eps'
+set fit errorvariables
+set xlabel "r"
+set ylabel "<n(r)n(0)>"
+
+plot "tV.dat" i 0  u 1:2:3 w e lc rgb "black"      lt 1 pt 7 lw 2 t "V/t=1" ,  \
+      ''      i 0  u 1:2   w l lc rgb "black"      lt 1      lw 2 t "" ,       \
+      ''      i 1  u 1:2:3 w e lc rgb "red"        lt 1 pt 7 lw 2 t "V/t=2" ,  \
+      ''      i 1  u 1:2   w l lc rgb "red"        lt 1      lw 2 t "" ,       \
+      ''      i 2  u 1:2:3 w e lc rgb "royalblue"  lt 1 pt 7 lw 2 t "V/t=2.5" ,\
+      ''      i 2  u 1:2   w l lc rgb "royalblue"  lt 1      lw 2 t ""
+
+!epstopdf tV.eps
+!evince tV.pdf
diff --git a/jupyterbook/uv.lock b/jupyterbook/uv.lock
new file mode 100644
index 0000000..b29deeb
--- /dev/null
+++ b/jupyterbook/uv.lock
@@ -0,0 +1,1176 @@
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