\documentclass{article}
\usepackage{blkarray} 
\newcommand{\matindex}[1]{\mbox{\scriptsize#1}} 
\begin{document}
\[
(‎H_{01})‎_{zig}=\begin{blockarray}{ccccccccccccc}
\matindex{$A _{1‎\uparrow‎} $} & \matindex{$A _{1‎‎\downarrow‎‎} $} & \matindex{$ B _{1‎\uparrow‎} $} &  \matindex{$ B _{1‎‎\downarrow‎‎} $} &  \matindex{$ A _{2‎\uparrow‎}  $} & \matindex{$ A _{2\downarrow‎‎} $} &  \matindex{$ B _{2‎\uparrow‎} $} & \matindex{$ B _{2‎‎\downarrow‎‎} $} & \matindex{$ A _{3‎\uparrow‎} $} & \matindex{$ A _{3‎‎\downarrow‎‎}  $} & \matindex{$  B _{3‎\uparrow‎}$} & \matindex{$ B _{3‎\downarrow‎‎} $} &\\
\begin{block}{(cccccccccccc)c}
0& 0 & -t &‎\frac{a‎\hbar\lambda(i-‎\sqrt{3})‎‎‎ }{4} & 0 & 0 & 0 & 0 & 0 & 3 & 0 & 0 & \matindex{$ \widetilde{A}‎‎^{+‎‎}‎ _{1‎\uparrow‎}     $}\\
0& 0 & ‎\frac{a‎\hbar\lambda(i+‎\sqrt{3})‎‎‎ }{4} & -t & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{A}‎^{+‎‎}_{1‎‎\downarrow‎‎} $} \\
0& ‎0‎‎ ‎ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{B}‎^{+‎‎}‎ _{1‎\uparrow‎} $}\\
0‎‎‎‎& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{B}^{+‎‎}_{1‎‎\downarrow‎‎}  $}\\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{A}‎^{+‎‎}‎ _{2‎\uparrow‎}    $} \\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{A}‎^{+‎‎}_{1‎2\downarrow‎‎} $}\\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$   \widetilde{B}‎^{+‎‎}‎ _{2‎\uparrow‎}  $}\\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \matindex{$   \widetilde{B}^{+‎‎}_{2\downarrow‎‎}$}\\
0& 0 & 0 & 0 & 0 & -t & ‎‎\frac{a‎\hbar\lambda(-i-‎\sqrt{3})‎‎‎ }{4} & 0 & 0 & 0 & 0 & 0 & \matindex{$  \widetilde{A}‎^{+‎‎}‎ _{3‎\uparrow‎}     $}\\
0& 0 & 0 & 0 &0  & ‎‎\frac{a‎\hbar\lambda(-i+‎\sqrt{3})‎‎‎ }{4}& -t & 0 & 0 & 0 & -t & ‎\frac{a‎\hbar\lambda(i-‎\sqrt{3})‎‎‎ }{4}& \matindex{$  \widetilde{A}‎^{+‎‎}_{3\downarrow‎‎} $}\\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & ‎‎\frac{a‎\hbar\lambda(i+‎\sqrt{3})‎‎‎ }{4} & -t& \matindex{$   \widetilde{B}‎^{+‎‎}‎ _{3‎\uparrow‎}  $}\\
0& 0 & 0 & 0 & 0 & 0 & 0 & 0 & ‎0 & 0 & 0 & 0 & \matindex{$   \widetilde{B}^{+‎‎}_{3\downarrow‎‎} $}\\
 \end{block}
 \end{blockarray}
 \]
\end{document}