Entanglement, combinatorics and finite-size effects in spin chains

We carry out a systematic study of the exact block entanglement in the XXZ spin chain at Δ = −1/2. We present the first analytic expressions for reduced density matrices for n spins in a chain of length L (for n≤6 and arbitrary but odd L) for a truly interacting model. The entanglement entropy and the moments of the reduced density matrix and its spectrum are then easily derived. We explicitly construct the 'entanglement Hamiltonian' as the logarithm of this matrix. Exploiting the degeneracy of the ground state, we find the scaling behavior of the entanglement of the zero-temperature mixed state.