Parity effects in the scaling of block entanglement in gapless spin chains

We consider the Rényi α entropies for Luttinger liquids (LL). For large block lengths ℓ, these are known to grow like lnℓ. We show that there are subleading terms that oscillate with frequency 2kF (the Fermi wave number of the LL) and exhibit a universal power-law decay with ℓ. The new critical exponent is equal to K/(2α), where K is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point