$\mathbb{Z}_{2}$ topological quantum paramagnet on a honeycomb bilayer

TL;DR

This paper demonstrates a honeycomb bilayer spin model hosting a $$ topological quantum paramagnet with protected edge states, revealing a new class of topological magnetic excitations influenced by spin-orbit coupling.

Contribution

It introduces a simple honeycomb bilayer model exhibiting a $$ topological quantum paramagnet with protected edge modes, and explores phase transitions to other topological states.

Findings

Identification of a $$ topological quantum paramagnet in a honeycomb bilayer model.

Calculation of edge states showing counterpropagating triplon modes.

Observation of a topological phase transition where the $$ index vanishes.

Abstract

Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected $\mathbb{Z}_2$ topological quantum paramagnet ({\em topological triplon insulator}) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial $\mathbb{Z}_2$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the $\mathbb{Z}_2$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the $\mathbb{Z}_2$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular d$^{4}$ Mott insulators, and their potential applications.