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How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and plaquette term $B(p)=\sigma_{p,1}^{z}\sigma_{p,2}^{z}\sigma_{p,3}^{z}\sigma_{p,4}^{z} $ ? Here $v$ are indices of vertices on a lattice with spin-1/2 particles on the edges, $p$ refers to the indices of the plaquettes in the lattice. enter image description here

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