Spin-wave study of entanglement and Rényi entropy for coplanar and collinear magnetic orders in two-dimensional quantum Heisenberg antiferromagnets

We use modified linear spin-wave theory (MLSWT) to study ground-state entanglement for a length-L line subsystem in L×L square- and triangular-lattice quantum Heisenberg antiferromagnets with coplanar spiral magnetic order with ordering vector Q=(q,q) and NG=3 Goldstone modes, except if q=π (collinear order, NG=2). Generalizing earlier MLSWT results for q=π to commensurate spiral order with s≥3 sublattices (q=2πr/s with r and s coprime), we find analytically for large L a universal and n-independent subleading term (NG/2)lnL in the Rényi entropy Sn, associated with L1/2 scaling of λ0 and λ±q, with λ0≠λ±q for spiral order; here {λky} are the L mode occupation numbers of the entanglement Hamiltonian. The term (3/2)lnL in Sn agrees with a nonlinear sigma model study of s=3 spiral order (q=2π/3). These and other properties of Sn and λky are explored numerically for an anisotropic nearest-neighbor triangular-lattice model for which q varies in the spiral phase.