Néel state

A Néel state is a two-sublattice product state with antiparallel spin polarization on the two sublattices. It is the classical ordered reference state of a bipartite antiferromagnet.

The Néel order parameter is the slowly varying staggered magnetization of an antiferromagnet. On a bipartite lattice it changes sign between neighboring sublattices before coarse graining.

For a linear spin-wave approximation, the ground state is empty of the diagonal quasiparticles but contains the original spin bosons. If $a_k=u_k{\alpha }_k-v_k{\alpha }_{-k}^{†}$, their occupation number is $v_k^2$. The staggered magnetization is reduced from $S$ to $S-N^{-1}{\sum }_k{v}_k^2$. For the one-dimensional nearest-neighbor Heisenberg antiferromagnet, $v_k^2=(|\sin k{|}^{-1}-1)/2$ and the integral diverges logarithmically. This invalidates finite ordered magnetization within the approximation; it is not itself a determination of the exact spectral gap.

At zero temperature, linear-mode vacuum depletion scales as $\int dk{k}^{d-2}$; at nonzero temperature Bose occupation changes this to $\int dk{k}^{d-3}$. The two convergence criteria are different.

For linear spin waves, $\delta S=(2N{)}^{-1}{\sum }_k[(1-{\gamma }_k^2{)}^{-1/2}-1]$. The chain has ${\gamma }_k=\cos k$ and a logarithmic infrared divergence. This signals failure of the ordered expansion, not a physical negative staggered moment.

The staggered magnetization weights the local magnetization with opposite signs on the two sublattices of a bipartite graph. It is nonzero in a Néel state even when the uniform magnetization vanishes.

The uniform magnetization is the nonalternating component of local spin polarization. In a nearly Néel-ordered antiferromagnet it describes the small canting shared by the two sublattices.