Gapped spin liquid with $\mathbb{Z}_2$-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on kagome lattice. We keep track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We use imaginary-time evolution to obtain the variational ground state, and use symmetric TRG to compute the modular matrices. We find that the ground state is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type). The correlation length is about 10 unit cell length.