Two dimensional Symmetry Protected Topological Phases with PSU(N) and time reversal symmetry

TL;DR

This paper investigates two-dimensional symmetry protected topological phases with PSU(N) and time reversal symmetry, describing their boundary properties and constructing a candidate wave function for a spin-1 system on a honeycomb lattice.

Contribution

It introduces a description of 2D SPT phases with PSU(N) and time reversal symmetry using a principal chiral model with a topological Theta-term and constructs a specific wave function candidate.

Findings

Boundary of the system is either gapless or degenerate when symmetries are preserved.

Constructed a wave function for a spin-1 system on honeycomb lattice as an SPT candidate.

Demonstrated the role of topological terms in classifying 2D SPT phases.

Abstract

Symmetry protected topological phase is one type of nontrivial quantum disordered many-body state of matter. In this work we study one class of symmetry protected topological phases in two dimensional space, with both PSU(N) and time reversal symmetry. These states can be described by a principal chiral model with a topological Theta-term. As long as the time-reversal symmetry and PSU(N) symmetry are both preserved, the 1+1 dimensional boundary of this system must be either gapless or degenerate. We will also construct a wave function of a spin-1 system on the honeycomb lattice, which is a candidate for the symmetry protected topological phase with both SO(3) and time-reversal symmetry.