Abstract
Starting with the valence-bond solid (VBS) ground state of the 1D AKLT Hamiltonian, we make a partition of the system in two subsystems A and B, where A is a block of L consecutive spins and B is its complement. In that setting we compute the partial transpose density matrix with respect to A, . We obtain the spectrum of the transposed density matrix of the VBS pure system. Subsequently, we define two disjoint blocks, A and B, containing LA and LB spins, respectively, separated by L sites. Tracing away the spins which do not belong to A∪B, we find an expression for the reduced density matrix of the A and B blocks, ρ(A, B). With this expression (in the thermodynamic limit), we compute the entanglement spectrum and other several entanglement measures, such as the purity P = tr(ρ(A, B)2), the negativity and the mutual entropy.
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