\documentclass[12pt]{article}
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\begin{document}
\begin{equation*}
    H = \sum_{i=1}^3 \Big[ \vec{B} \cdot \vec{\sigma}_i
    +\lambda^{(1)} Z_i Z_{i+1} + \lambda^{(2)}
    (X_i X_{i+1} +Y_i Y_{i+1})  \Big].
\end{equation*}
\end{document}