1209.4399 (Cenke Xu)

Three dimensional Symmetry Protected Topological Phase close to
Antiferromagnetic Neel order    [PDF]

Cenke Xu

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 3+1 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 fourth homotopy group Pi4[M] = Z for N > 1, this NLSM can naturally have a Theta-term. We will argue that when Theta = 2Pi this NLSM describes a SPT phase. We will also construct a lattice model for this SPT phase, whose long wavelength physics is precisely described by this NLSM with Theta = 2Pi. This SPT phase is protected by the SU(2N) spin symmetry, without assuming any lattice symmetry.

View original: http://arxiv.org/abs/1209.4399