Three dimensional Symmetry Protected Topological Phase close to Antiferromagnetic Neel order

Understand

It is well-known that the Haldane phase of one-dimensional spin-1 chain is a symmetry protected topological (SPT) phase, which is described by a nonlinear Sigma model (NLSM) with a Theta-term at Theta = 2Pi.

• In this work we study a three dimensional SPT phase of SU(2N) antiferromagnetic spin system with a self-conjugate representation on every site.
• The spin ordered Neel phase of this system has a ground state manifold M = U(2N)/[U(N)xU(N)], and this system is described by a NLSM defined with manifold M.
• Since the homotopy group Pi4[M] = Z for N > 1, this NLSM can naturally have a Theta-term.