update docs for su2 to sz

docs/source/tutorial/qc-hamiltonians.ipynb

@@ -2107,7 +2107,11 @@
         "\n",
         "We can also transform the spin-adapted MPS generated in the ``SU2`` mode to the non-spin-adapted MPS, which can be used in the ``SZ`` mode. After obtaining the non-spin-adapted MPS, one need to redo ``driver.initialize_system``, ``driver.get_qc_mpo``, etc. to make sure every object is now represented in the ``SZ`` mode, then you can operate on the ``SZ`` non-spin-adapted MPS.\n",
         "\n",
-        "In the following example, we first compute the spin-adapted MPS, then translate it into the non-spin-adapted MPS to extract the determinant coefficients."
+        "In the following example, we first compute the spin-adapted MPS, then translate it into the non-spin-adapted MPS to extract the determinant coefficients.\n",
+        "\n",
+        "As the transform from SU2 format to SZ format is only implemented for left canonicalized MPS, we need to add a line ``driver.align_mps_center(ket, ref=0)`` to change its canonical center to zero (if it is not zero) before translating an MPS from SU2 format to SZ format.\n",
+        "\n",
+        "For a non-singlet SU2 MPS (not the case in the example below), as it can have multiple SZ components, we need to specify a specific SZ component. This is done via the ``sz`` argument of ``driver.mps_change_to_sz``. When we extract only a component of the non-singlet SU2 MPS, the norm of the extracted MPS will be smaller than the norm of the original SU2 MPS. Therefore, one may explicitly compute the ``norm**2`` of the translated MPS (using ``driver.expectation(zket, driver.get_identity_mpo(), zket)``), and the computed PDM quantities should be scaled by ``1 / norm**2``. Quantities like orbital entropies have to be computed after the MPS is normalized. MPSs can be normalized using ``zket.iscale(1 / norm)``."
       ]
     },
     {
@@ -2202,6 +2206,7 @@
         "    thrds=thrds, iprint=1)\n",
         "print('DMRG energy = %20.15f' % energy)\n",
         "\n",
+        "driver.align_mps_center(ket, ref=0)\n",
         "csfs, coeffs = driver.get_csf_coefficients(ket, cutoff=0.05, iprint=1)\n",
         "zket = driver.mps_change_to_sz(ket, \"ZKET\")\n",
         "\n",