Possible phases of the spin- 12 XXZ model on a honeycomb lattice by boson-vortex duality

Abstract

Motivated by recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-1 2 J1 − J2 XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various gapped phases that either break certain lattice symmetry or preserve all the symmetries. The gapped phases breaking lattice symmetries occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase, while condensing both vortex flavors gives rise to a valence-bond-solid state. Both of those phases have been observed in the numerical studies of the J1 − J2 XXZ honeycomb model. Furthermore, by tuning the band structure of vortex and condensing it at the Γ point, we obtain a featureless paramagnet. But the precise nature of this featureless state is still unclear and needs future study.

Quantum correlations in the frustrated XY model on the honeycomb lattice

“…The framework of boson-vortex duality has been used to scrutinise the above model, showing that the condensation of one of the two vortex flavours corresponds to the emergence of the Ising phase in the intermediate region. Conversely, the condensation of both vortex flavours leads to the replacement of the QSL 38 . Furthermore, the field of bosonic dynamical mean-field theory has recognised the emergence of an emergent chiral spin state in the intermediate frustration regime, replacing the dominance of both the Ising and QSL phases 39 .…”