Abstract
Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Néel ordered 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 Nambu-Goldstone modes give additive logarithmic corrections with a prefactor independent of the Rényi index. On the other hand, corners lead to additional (negative) logarithmic corrections with a prefactor which does depend on both and the Rényi index , in good agreement with scalar field theory predictions. By varying the second neighbor coupling we also explore universality across the Néel ordered side of the phase diagram of the antiferromagnet, from the frustrated side where the area law term is maximal, to the strongly ferromagnetic regime with a purely logarithmic growth , thus recovering the mean-field limit for a subsystem of sites. Finally, a universal subleading constant term is extracted in the case of strip subsystems, and a direct relation is found (in the large- limit) with the same constant extracted from free lattice systems. The singular limit of vanishing aspect ratios is also explored, where we identify for a regular part and a singular component, explaining the discrepancy of the linear scaling term for fixed width vs fixed aspect ratio subsystems.
11 More- Received 14 June 2015
DOI:https://doi.org/10.1103/PhysRevB.92.115126
©2015 American Physical Society