fix docs

docs/source/tutorial/custom-hamiltonians.ipynb

@@ -891,9 +891,9 @@
         "$$\n",
         "\\hat{H} = \\sum_{i=1}^{L-1} \\Big( \\frac{1}{2} S^+_{i} S^-_{i+1} + \\frac{1}{2} S^-_{i} S^+_{i+1} + S^z_{i} S^z_{i+1} \\Big)\n",
         "$$\n",
-        "using $U(1) \\times Z_2$ (projected spin $\\hat{S}_z$ and spatial reflection $\\hat{R}$) symmetry.\n",
+        "using $U(1) \\times Z_2$ (projected spin $\\hat{S}_z$ and spatial reflection $\\hat{R}$ about the center of the chain) symmetry.\n",
         "\n",
-        "First, we need to transform the local states so that they have well defined quantum numbers in the $U(1) \\times Z_2$ symmetry group. Consider a two-site system. The states can be represented as $|\\alpha\\alpha\\rangle, |\\alpha\\beta\\rangle, |\\beta\\alpha\\rangle$, and $|\\beta\\beta\\rangle$. Since $\\hat{R} |\\alpha\\beta\\rangle = |\\beta\\alpha\\rangle $, states $|\\alpha\\beta\\rangle$ and $|\\beta\\alpha\\rangle$ do not have well-defined quantum number for $\\hat{R}$. Therefore, we define the following four local states for the two-site system:\n",
+        "First, we need to transform the local states so that they have well defined quantum numbers in the $U(1) \\times Z_2$ symmetry group. Consider a two-site system. The states can be represented as $|\\alpha\\alpha\\rangle,|\\alpha\\beta\\rangle,|\\beta\\alpha\\rangle$, and $|\\beta\\beta\\rangle$. Since $\\hat{R}|\\alpha\\beta\\rangle=|\\beta\\alpha\\rangle$, states $|\\alpha\\beta\\rangle$ and $|\\beta\\alpha\\rangle$ do not have well-defined quantum number for $\\hat{R}$. Therefore, we define the following four local states for the two-site system:\n",
         "\n",
         "$$\n",
         "|0\\rangle = |\\alpha\\alpha\\rangle,\\quad\n",