Universal logarithmic correction in the Renyi entropy for the spin-$S$ Heisenberg quantum antiferromagnet on the square and triangular lattices: a modified spin-wave theory study

Recently there has been much interest in a signature of broken continuous symmetry in the Renyi entropy, in the form of a universal term that diverges logarithmically with the subsystem size and is proportional to the number of Goldstone modes $n_G$ [1]. Here we use modified spin-wave theory to study the Renyi entropy for the spin-$S$ Heisenberg quantum antiferromagnet on the square and triangular lattices. By considering a one-dimensional (line) subsystem of length $L$ that wraps around an $L \times L$ torus, the eigenvalues of the reduced density matrix can be found analytically. Focusing especially on the part of the Renyi entropy that is independent of the Renyi index, we find that it contains a universal term $(n_G/2)\log L$ (where $n_G=2,3$ for the square and triangular lattice model, respectively) as well as an ''area law'' contribution $\propto L$. We also discuss the dependence on the spin $S$. We compare our findings with previous related works [1,2].

[1] M. A. Metlitski and T. Grover, arXiv:1112.5166v2.
[2] D. J. Luitz et al., Phys. Rev. B 91, 155145 (2015); N. Laflorencie et al., Phys. Rev. B 92, 115126 (2015); L. Rademaker, Phys. Rev. B 92, 144419 (2015).