Topologically different spin disorder phases of the J1-J2 Heisenberg model on the honeycomb lattice

Abstract: Searching for spin liquids on the honeycomb J1-J2 Heisenberg model has been attracting great attention in the past decade. In this Paper we investigate the topological properties of the J1-J2 Heisenberg model by introducing nearest-neighbour and next-nearest-neighbour bond parameters. We find that there exist two topologically different phases in the spin disordered regime 0.2<J2/J1\<0.5: for J2/J1\<0.32, the system is a zero-flux spin liquid which is topological trivial and gapless; for J2/J1\>0.32, it is a pi-flux chiral spin liquid, which is topological nontrivial and gapped. These results suggest that there exist two topologically different spin disorder phases in honeycomb J1-J2 Heisenberg model.