Spin-wave approach for entanglement entropies of the J1-J2 Heisenberg antiferromagnet on the square lattice

Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Neel ordered J(1)-J(2) Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the n(G) = 2 Nambu-Goldstone modes give additive logarithmic corrections with a prefactor n(G)/2 independent of the Renyi index. On the other hand, pi/2 corners lead to additional (negative) logarithmic corrections with a prefactor l(q)(c) which does depend on both n(G) and the Renyi index q, in good agreement with scalar field theory predictions. By varying the second neighbor coupling J(2) we also explore universality across the Neel ordered side of the phase diagram of the J(1)-J(2) antiferromagnet, from the frustrated side 0 < J(2)/J(1) < 1/2 where the area law term is maximal, to the strongly ferromagnetic regime - J(2)/J(1) >> 1 with a purely logarithmic growth S-q = n(G) 2 ln N, thus recovering the mean-field limit for a subsystem of N sites. Finally, a universal subleading constant term gamma(ord)(q) is extracted in the case of strip subsystems, and a direct relation is found (in the large-S limit) with the same constant extracted from free lattice systems. The singular limit of vanishing aspect ratios is also explored, where we identify for gamma(ord)(q) a regular part and a singular component, explaining the discrepancy of the linear scaling term for fixed width vs fixed aspect ratio subsystems.