Interplay of entanglement measures and transport phenomena in the Haldane model of Dirac magnons

We investigate the interplay between quantum entanglement and transport phenomena in a noninteracting bosonic system described by a honeycomb ferromagnet. In particular, we analyze the effects of an external magnetic field and the Dzyaloshinskii–Moriya interaction (DMI), which opens a topological gap in the magnon spectrum and induces a Chern–Simons effective action for the elastic degrees of freedom. Their combined influence is examined through the mixed-state entanglement measure provided by the entanglement negativity.

We compute the entanglement spectrum and the entanglement negativity as functions of temperature and magnetic field strength to elucidate how DMI-induced modifications in the magnon bands affect quantum correlations. In parallel, we study the system’s thermal and spin Hall transport properties, with particular emphasis on the spin Nernst coefficient. Finally, we analyze how transport signatures, such as the spin Nernst response, correlate with and influence entanglement negativity.