add quantum number tutorial

fix mps random quantum number

doc/source/applications.rst

@@ -1,6 +1,8 @@
 Application Tutorials
 =====================
 
+More tutorials are coming!
+
 .. toctree::
     tutorials/1D-Heisenberg.ipynb
 

doc/source/tutorial.rst

@@ -9,11 +9,10 @@ please refer to the :doc:`applications`.
     tutorials/define_model.ipynb
     tutorials/mps_mpo.ipynb
     tutorials/compress_mps.ipynb
+    tutorials/quantum_number.ipynb
     tutorials/ttn_basic.ipynb
 
 ..
-    setting quantum number
-    compress mps (done)
     finding the ground state
     time evolution by hand forward Euler
     time evolutions in production

doc/source/tutorials/compress_mps.ipynb

@@ -7,7 +7,7 @@
    "source": [
     "# Compressing MPS\n",
     "## Overview\n",
-    "MPS can efficiently compress the system wavefunction."
+    "In this notebook we will show how to compress the wavefuntion stored in an MPS via singular value decomposition (SVD)."
    ]
   },
   {
@@ -20,7 +20,7 @@
     "The model we use is a Frenkel-Holstein model with 3 electronic sites and 2 vibration modes for each electronic site\n",
     "\n",
     "$$\n",
-    "\\hat H = \\sum_{i=1}^3\\sum_{j=1}^3 J_{ij} \\hat a^\\dagger_i a_{i+1} + \\sum_{i=1}^3\\sum_{k=1,2}\\frac{1}{2}  (\\hat p_{ik}^2 + \\omega_k^2 \\hat x_{ik}^2) + \\sum_{i=1}^3\\sum_{k=1,2} \\hat a^\\dagger_i \\hat a_i \\hat x_{ik}\n",
+    "\\hat H = \\sum_{i=1}^3\\sum_{j=1}^3 J_{ij} \\hat a^\\dagger_i \\hat a_{i+1} + \\sum_{i=1}^3\\sum_{k=1,2}\\frac{1}{2}  (\\hat p_{ik}^2 + \\omega_k^2 \\hat x_{ik}^2) + \\sum_{i=1}^3\\sum_{k=1,2} \\hat a^\\dagger_i \\hat a_i \\hat x_{ik}\n",
     "$$\n",
     "\n",
     "Therefore, the model has 9 sites in total. 3 of them are electronic sites and the rest are vibrational sites."
@@ -504,4 +504,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}