Spin quantum Hall effects in a spin-1 topological paramagnet

TL;DR

This paper demonstrates how to realize gapped bulk states with protected gapless edge states exhibiting spin quantum Hall effects in spin-1 topological paramagnets on 2D lattices, using fermion representations and specific Hamiltonians.

Contribution

It introduces a method to realize spin-1 topological paramagnets with protected edge states and spin quantum Hall effects on 2D lattices, including a concrete kagome lattice example.

Findings

Gapped bulk states with gapless edge modes protected by spin symmetry.

Concrete fermion-based model on kagome lattice.

Proposal of a microscopic Hamiltonian for realization.

Abstract

AKLT state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets, which hosts symmetry-protected gapless excitations on the boundary. In this work we show how to realize this type of featureless spin-1 states on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk but supports gapless edge states protected by spin rotational symmetry along a certain direction, and are featured by spin quantum Hall effect. Using fermion representation of integer-spins we show a concrete example of such spin-1 topological paramagnets on kagome lattice, and suggest a microscopic spin-1 Hamiltonian which may realize it.