fix: split multi-line KaTeX display block into two separate $$ blocks

\\ (newline) inside a bare $$ block is not valid in older KaTeX versions.
Splitting into two consecutive $$ blocks achieves the same visual result
without relying on environment-level line breaks.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: egull

content/en/documentation/methods/ed/symmetry.md

@@ -75,7 +75,9 @@ Finally, we diagonalize each block of the Hamiltonian to obtain the eigenvalues
 The $S^z_{\text{total}} = 0$ sector consists of states with exactly 2 spins up ($\uparrow$) and 2 spins down ($\downarrow$). For a 4-site chain, there are $\binom{4}{2} = 6$ basis states in this sector:
 
 $$
-|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle, \\
+|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle
+$$
+$$
 |\psi_4\rangle = |\downarrow, \uparrow, \uparrow, \downarrow\rangle, \quad |\psi_5\rangle = |\downarrow, \uparrow, \downarrow, \uparrow\rangle, \quad |\psi_6\rangle = |\downarrow, \downarrow, \uparrow, \uparrow\rangle
 $$
 

content/ja/documentation/methods/ed/symmetry.md

@@ -75,7 +75,9 @@ Finally, we diagonalize each block of the Hamiltonian to obtain the eigenvalues
 The $S^z_{\text{total}} = 0$ sector consists of states with exactly 2 spins up ($\uparrow$) and 2 spins down ($\downarrow$). For a 4-site chain, there are $\binom{4}{2} = 6$ basis states in this sector:
 
 $$
-|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle, \\
+|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle
+$$
+$$
 |\psi_4\rangle = |\downarrow, \uparrow, \uparrow, \downarrow\rangle, \quad |\psi_5\rangle = |\downarrow, \uparrow, \downarrow, \uparrow\rangle, \quad |\psi_6\rangle = |\downarrow, \downarrow, \uparrow, \uparrow\rangle
 $$
 

content/zh-cn/documentation/methods/ed/symmetry.md

@@ -75,7 +75,9 @@ Finally, we diagonalize each block of the Hamiltonian to obtain the eigenvalues
 The $S^z_{\text{total}} = 0$ sector consists of states with exactly 2 spins up ($\uparrow$) and 2 spins down ($\downarrow$). For a 4-site chain, there are $\binom{4}{2} = 6$ basis states in this sector:
 
 $$
-|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle, \\
+|\psi_1\rangle = |\uparrow, \uparrow, \downarrow, \downarrow\rangle, \quad |\psi_2\rangle = |\uparrow, \downarrow, \uparrow, \downarrow\rangle, \quad |\psi_3\rangle = |\uparrow, \downarrow, \downarrow, \uparrow\rangle
+$$
+$$
 |\psi_4\rangle = |\downarrow, \uparrow, \uparrow, \downarrow\rangle, \quad |\psi_5\rangle = |\downarrow, \uparrow, \downarrow, \uparrow\rangle, \quad |\psi_6\rangle = |\downarrow, \downarrow, \uparrow, \uparrow\rangle
 $$