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We consider the Rényi α-entropies for Luttinger liquids (LL). For large block lengths these are known to grow like ln . 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 . 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.PACS numbers: 64.70. Tg, 03.67.Mn, 75.10.Pq, 05.70.Jk Luttinger liquid (LL) theory describes the low-energy (large-distance) physics of gapless one-dimensional models such as quantum spin chains and correlated electron models. It corresponds to a conformal field theory (CFT) with central charge c = 1 and is known to provide accurate predictions for universal properties of many physical systems. LL theory has been applied successfully to recent experiments on carbon nanotubes [1], spin chains [2], and cold atomic gases [3]. A much studied example of a lattice model that gives rise to a LL description at low energies is the spin-1/2 Heisenberg XXZ chainHere σ j are Pauli matrices at site j and we have imposed periodic boundary conditions. Recent years have witnessed a significant effort to quantify the degree of entanglement in many-body systems (see e.g.[4] for reviews). Among the various measures, the entanglement entropy (EE) has been by far the most studied. By partitioning an extended quantum system into two subsystems, the EE is defined as the von Neumann entropy of the reduced density matrix ρ A of one of the subsystems. The leading contribution to the EE of a single, large block of length can be derived by general CFT methods [5][6][7]. The case of a subsystem consisting of multiple blocks requires a model dependent treatment, but the EE can still be obtained from CFT [8]. On the other hand, little is known with regard to corrections to the leading asymptotic behaviour. In the following we consider the Rényi entropieswhich give the full spectrum of ρ A [9] and are fundamental for understanding the scaling of algorithms based on matrix product states [10][11][12]. We note that S 1 is the von Neumann entropy and S ∞ gives minus the logarithm of the maximum eigenvalue of the reduced density matrix (known as single copy entanglement [13,14] where c is the central charge and c α a non-universal constant. In a finite system of length L, the block length in (3) should be replaced with the chord dis-In many lattice models the asymptotic scaling is obscured by large oscillations proportional to (−1) . Some typical examples are shown in Fig. 1, where we plot S α ( , L) for α = 1, 2, ∞ for the XXZ model at ∆ = −1/2 as obtained by density matrix renormalization group (DMRG) computations. While S 1 is smooth, S α =1 is seen to exhibit large oscillations. For α = ∞ in particular it is difficult to recognize the CFT scaling behaviour (3). While such oscillations have been observed in several examples [15,16] and can be seen to arise from strong antiferrom...