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@@ -1298,12 +1298,14 @@ <h3 id="subproblems">Subproblems</h3>
 Source: Haldane, F. D. M. (1988). Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the" parity anomaly". Physical review letters, 61(18).</p>
 <p>We denote <span class="arithmatex">\(\{\mathbf{a}_i\}\)</span> are the vectors from a B site to its three nearest-neighbor A sites, and <span class="arithmatex">\(\{\mathbf{b}_i\}\)</span> are next-nearest-neighbor distance vectors, then we have
 $$
-{\mathbf{a}_1} = (0,a),\
-{\mathbf{a}_2} = (\sqrt 3 a/2, - a/2),\
-{\mathbf{a}_3} = ( - \sqrt 3 a/2, - a/2)\
-{\mathbf{b}_1} = {\mathbf{a}_2} - {\mathbf{a}_3} = (\sqrt 3 a,0),\
-{\mathbf{b}_2} = {\mathbf{a}_3} - {\mathbf{a}_1} = ( - \sqrt 3 a/2, - 3a/2),\
-{\mathbf{b}_3} = {\mathbf{a}_1} - {\mathbf{a}_2} = ( - \sqrt 3 a/2,3a/2)
+\begin{aligned}
+{\mathbf{a}_1} &amp;= (0,a),\
+{\mathbf{a}_2} &amp;= (\sqrt 3 a/2, - a/2),\
+{\mathbf{a}_3} &amp;= ( - \sqrt 3 a/2, - a/2)\
+{\mathbf{b}_1} &amp;= {\mathbf{a}_2} - {\mathbf{a}_3} = (\sqrt 3 a,0),\
+{\mathbf{b}_2} &amp;= {\mathbf{a}_3} - {\mathbf{a}_1} = ( - \sqrt 3 a/2, - 3a/2),\
+{\mathbf{b}_3} &amp;= {\mathbf{a}_1} - {\mathbf{a}_2} = ( - \sqrt 3 a/2,3a/2)
+\end{aligned}
 $$</p>
 <p>Then the Haldane model on a hexagonal lattice can be written as
 <span class="arithmatex">\(<span class="arithmatex">\(H(k) = {d_0}I + {d_1}{\sigma _1} + {d_2}{\sigma _2} + {d_3}{\sigma _3}\)</span>\)</span>