Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature

Abstract

We theoretically investigate, within the Schwinger-Boson mean-field theory, the transition from a gapped $Z_2$ quantum spin-liquid, in a $J_1$-$J_2$ Heisenberg spin-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 $J_{\chi }$), with non-trivial Chern bands of the excitations. We numerically obtain a phase diagram of such $J_1$-$J_2$-$J_{\chi }$ system, where different phases 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 non-trivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to large thermal Hall coefficient.

12 pages, 7 figures. Comments welcome; clarified that the state we obtain is a chiral Z_2 spin liquid state with non-zero Chern numbers of the excitation bands

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