QUROPE Quantum Information Processing and Communication in Europe

We examine, using density matrix renormalization group (DMRG) algorithm and finite size scaling theory, the behavior of the entanglement spectrum in the vicinity of the Haldane phase for spin-1 chains. We show that the difference between the two largest coefficients in the entanglement spectrum, the Schmidt gap, scales up to small logarithmic corrections, with universal critical exponents when approaching a quantum phase transition, yielding a further link between entanglement theory and conformal field theory. Furthermore, our results indicate that in the vicinity of the Haldane phase, the Schmidt gap behaves as a local order parameter.