This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.
Variation of Topological Edge States of 2D Honeycomb Lattice Photonic Crystals