Three dimensional Symmetry Protected Topological Phase close to Antiferromagnetic Neel order

TL;DR

This paper explores a three-dimensional symmetry protected topological (SPT) phase in SU(2N) antiferromagnetic spin systems, characterized by a nonlinear Sigma model with a Theta-term at 2Pi, protected by SU(2N) symmetry.

Contribution

It introduces a 3D SPT phase described by a nonlinear Sigma model with a Theta-term at 2Pi, extending the understanding of topological phases in higher dimensions.

Findings

The NLSM with Theta=2Pi describes a 3D SPT phase.

The SPT phase is protected by SU(2N) symmetry or its subgroup.

A lattice spin state is constructed matching the NLSM description.

Abstract

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. We will argue that when Theta = 2Pi this NLSM describes a SPT phase. This SPT phase is protected by the SU(2N) spin symmetry, or its subgroup SU(N)xSU(N)xZ2, without assuming any other discrete symmetry. We will also construct a trial SU(2N) spin state on a 3d lattice, we argue that the long wavelength physics of this state is precisely described by the aforementioned NLSM with Theta = 2Pi.