Schwinger-boson mean-field study of the spin-$1/2 {J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{\ensuremath{\chi}}$ model in the honeycomb lattice: Thermal Hall signature

Schwinger-boson mean-field study of the spin- $1 / 2 J_{1} − J_{2} − J_{χ}$ model in the honeycomb lattice: Thermal Hall signature

Rohit Mukherjee, Ritajit Kundu, Avinash Singh, and Arijit Kundu

Phys. Rev. B 107, 155122 – Published 11 April 2023

Abstract

We theoretically investigate, within Schwinger-boson mean-field theory, the transition from a gapped $Z_{2}$ quantum spin liquid, in a $J_{1} − J_{2}$ Heisenberg spin- $\frac{1}{2}$ system in a honeycomb lattice, to a chiral $Z_{2}$ spin-liquid phase under the presence of time-reversal symmetry-breaking scalar chiral interaction (with amplitude $J_{χ}$ ). We numerically obtain a phase diagram of this $J_{1} − J_{2} − J_{χ}$ system, where different ground states are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation, and the symmetries of the mean-field parameters. The chiral $Z_{2}$ state is characterized by the nontrivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to a large thermal Hall coefficient.